Some inequalities in connection to relative orders of entire functions of several complex variables
|
|
- Crystal Stone
- 5 years ago
- Views:
Transcription
1 Int. J. Nonlinear Anal. Appl. 7 (2016) No. 2, ISSN: (electronic) Some inequalities in connection to relative orders of entire functions of several complex variables Sanjib Kumar Datta a,, Tanmay Biswas b, Debasmita Dutta c a Department of Mathematics, University of Kalyani, P.O. Kalyani, Dist-Nadia,PIN , West Bengal, India b Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia,PIN , West Bengal, India c Mohanpara Nibedita Balika Vidyalaya (High),P.o - Amrity, Block - English Bazar, Dist.- District - Malda, PIN , West Bengal, India (Communicated by A. Ebadian) Abstract Let f, g h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order relative lower order of f with respect to g when the relative orders relative lower orders of both f g with respect to h are given. Keywords: entire function; several complex variables; relative order; relative lower order MSC: Primary 32A15; Secondary 30D Introduction preliminaries Let f be an entire function of two complex variables holomorphic in the closed polydisc U = {(z 1, z 2 ) : z i r i, i = 1, 2 for all r 1 0, r 2 0} M f (r 1, r 2 ) = max { f (z 1, z 2 ) : z i r i, i = 1, 2}. Then in view of maximum principal Hartogs theorem {[7], p. 2, p. 51}, M f (r 1, r 2 ) is an increasing functions of r 1, r 2. The following definition is well known: Definition 1.1. {[7], p. 339, (see also [1])} The order v2 ρ f the lower order v2 λ f of an entire function f of two complex variables are defined as log [2] M f (r 1, r 2 ) v 2 ρ f = r 1,r 2 log (r 1 r 2 ) log [2] M f (r 1, r 2 ) v2 λ f = lim inf, r 1,r 2 log (r 1 r 2 ) Corresponding author addresses: sanjib_kr_datta@yahoo.co.in (Sanjib Kumar Datta), tanmaybiswas_math@rediffmail.com (Tanmay Biswas), debasmita.dut@gmail.com (Debasmita Dutta) Received: July 2015 Revised: October 2016
2 134 Datta, Biswas, Dutta ( ) where log [k] x = log log [k 1] x, k = 1, 2, 3,... log [0] x = x. If we consider the above definiton for single variable, then the definition coincides with the classical definition of order (see [14]) which is as follows: Definition 1.2. ([14]) The order ρ f the lower order λ f of an entire function f are defined in the following way: log [2] M f (r) ρ f = r log r where M f (r) = max { f (z) : z = r}. λ f = lim inf r log [2] M f (r), log r If f is non-constant then M f (r) is strictly increasing continuous, its inverse f : ( f (0), ) (0, ) exists is such that lim f (s) =. Bernal {[2], [3]} introduced the s definition of relative order of g with respect to f, denoted by ρ f (g) as follows : ρ g (f) = inf {µ > 0 : M f (r) < (r µ ) for all r > r 0 (µ) > 0} = 1 M f (r). r log r The definition coincides with the classical one [14] if g (z) = exp z. During the past decades, several authors ( see [5],[9],[10],[11],[12],[13]) made close investigations on the properties of relative order of entire functions of single variable. In the case of relative order, it was then natural for Banerjee Dutta [4] to define the relative order of entire functions of two complex variables as follows: Definition 1.3. ([4]) The relative order between two entire functions of two complex variables denoted by v2 ρ g (f) is defined as: v 2 ρ g (f) = inf {µ > 0 : M f (r 1, r 2 ) < (r µ 1, r µ 2 ) ; r 1 R (µ), r 2 R (µ)} = 1 M f (r 1, r 2 ) r 1,r 2 log (r 1 r 2 ) where f g are entire functions holomorphic in the closed polydisc U = {(z 1, z 2 ) : z i r i, i = 1, 2 for all r 1 0, r 2 0} the definition coincides with Definition 1.1 {see [4]} if g (z) = exp (z 1 z 2 ). Extending this notion, Dutta [6] introduced the idea of relative order of entire functions of several complex variables in the following way: Definition 1.4. ([6]) Let f(z 1, z 2,..., z n ) g(z 1, z 2,..., z n ) be any two entire functions of n complex variables z 1, z 2,..., z n with maximum modulus functions M f (r 1, r 2,..., r n ) (r 1, r 2,..., r n ) respectively then the relative order of f with respect to g, denoted by vn ρ g (f) is defined by ρ g (f) = inf {µ > 0 : M f (r 1, r 2,..., r n ) < (r µ 1, r µ 2,..., r µ n) ; for r i R (µ), i = 1, 2,..., n}.
3 Some inequalities in connection to relative orders... 7 (2016) No. 2, The above definition can equivalently be written as 1 M f (r 1, r 2,..., r n ) ρ g (f) =. r 1,r 2,...,r n Similarly, one can define the relative lower order of f with respect to g denoted by vn λ g (f) as follows: 1 M f (r 1, r 2,..., r n ) λ g (f) = lim inf. r 1,r 2,...,r n If we consider g(z 1, z 2,..., z n ) = exp (z 1 z 2...z n ), then Definition 1.4 reduces to the following classical definition of order lower order in connection with several complex variables: Definition 1.5. The order vn ρ f the lower order vn λ f of an entire function f of two complex variables are defined as log [2] M f (r 1, r 2,..., r n ) ρ f = r 1,r 2,...,r n log [2] M f (r 1, r 2,..., r n ) λ f = lim inf. r 1,r 2,...,r n Also an entire function of several complex variables for which order lower order are the same is said to be of regular growth. The function exp (z 1 z 2...z n ) is an example of regular growth of entire function of several complex variables. Further the functions which are not of regular growth are said to be of irregular growth. Similarly for an entire function of several complex variables for which relative order relative lower order with respect to another entire function of several complex variables are the same is said to be of regular relative growth with respect to that entire function. Also the functions which are not of regular relative growth with respect to entire functions are said to be of irregular relative growth with respect to respective entire functions. Now a question may arise about relative order (relative lower order) of f with respect to another entire function g when relative order (relative lower oreder) of f g with respect to another entire function h are respectively given. In this paper we intend to provide this answer. Interested researchers may also think over to establish such type of results on the coupled systems of equations with entire polynomial functions {cf. [8]}. We do not explain the stard definitions notations in the theory of entire function of two complex variables as those are available in [7]. 2. The main results In this section we present the main results of the paper. Theorem 2.1. Let f, g h be any three entire functions of several complex variables such that relative order (relative lower order) of f with respect to h relative order (relative lower order) of f with respect to h are vn ρ h (f) ( vn λ h (f)) vn ( vn λ h (g)) respectively. Then { } λ h (f) v λ g (f) min n λ h (f) λ h (g), ρ { max λ h (f) λ h (g), ρ } vn ρ g (f) vn ρ h (f) λ h (g).
4 136 Datta, Biswas, Dutta Proof. From the definitions of vn ρ h (f) vn λ h (f), we have for all sufficiently large values of r 1, r 2,..., r n that h M f (r 1, r 2,..., r n ) exp {( vn ρ h (f) + ε) } M f (r 1, r 2,..., r n ) M h {( vn ρ h (f) + ε) }], (2.1) h M f (r 1, r 2,..., r n ) exp {( vn λ h (f) ε) } M f (r 1, r 2,..., r n ) M h {( vn λ h (f) ε) }], (2.2) also for a sequence of values of r 1, r 2,..., r n tending to infinity we get that h M f (r 1, r 2,..., r n ) exp {( vn ρ h (f) ε) } M f (r 1, r 2,..., r n ) M h {( vn ρ h (f) ε) }], (2.3) h M f (r 1, r 2,..., r n ) exp {( vn λ h (f) + ε) } M f (r 1, r 2,..., r n ) M h {( vn λ h (f) + ε) }]. (2.4) Similarly from the definitions of vn vn λ h (g), it follows for all sufficiently large values of r 1, r 2 that h (r 1, r 2,..., r n ) exp {( vn + ε) } (r 1, r 2,..., r n ) M h {( vn + ε) }] M h (r 1, r 2,..., r n ) [ log (r1 r 2...r n ) ( vn + ε) ]]. (2.5) h (r 1, r 2,..., r n ) exp {( vn λ h (g) ε) } (r 1, r 2,..., r n ) M h {( vn λ h (g) ε) }] log (r1 r 2...r n ) M h (r 1, r 2,..., r n ) ( vn λ h (g) ε) for a sequence of values of r 1, r 2,..., r n tending to infinity we obtain that (2.6) h (r 1, r 2,..., r n ) exp {( vn ε) } (r 1, r 2,..., r n ) M h {( vn ε) }] M h (r 1, r 2,..., r n ) [ log (r1 r 2...r n ) ( vn ε) ]]. (2.7) h (r 1, r 2,..., r n ) exp {( vn λ h (g) + ε) } (r 1, r 2,..., r n ) M h {( vn λ h (g) + ε) }] M h (r 1, r 2,..., r n ) [ log (r1 r 2...r n ) ( vn λ h (g) + ε) ]]. (2.8) Now from (2.3) in view of (2.5), we get for a sequence of values of r 1, r 2,..., r n tending to infinity that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn ρ h (f) ε) }]
5 Some inequalities in connection to relative orders... 7 (2016) No. 2, M f (r 1, r 2,..., r n ) 1 vn ρ h (f) ε) } ( vn + ε) 1 M f (r 1, r 2,..., r n ) ( ρ h (f) ε) ( vn + ε) log (r 1r 2...r n ) log As ε (> 0) is arbitrary, it follows that ( ρ h (f) ε) ( vn + ε). 1 M f (r 1, r 2,..., r n ) ρ r 1,r 2 ρ vn ρ g (f). (2.9) Analogously, from (2.2) in view of (2.8) it follows for a sequence of values of r 1, r 2,..., r n tending to infinity that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn λ h (f) ε) }] 1 M f (r 1, r 2,..., r n ) 1 vn λ h (f) ε) } ( vn λ h (g) + ε) 1 M f (r 1, r 2,..., r n ) ( λ h (f) ε) ( vn λ h (g) + ε) log (r 1r 2...r n ) log ( λ h (f) ε) ( vn λ h (g) + ε). Since ε (> 0) is arbitrary, we get from above that 1 M f (r 1, r 2,..., r n ) λ r 1,r 2 λ h (g) λ vn ρ g (f) λ h (g). (2.10) Again in view of (2.6), we have from (2.1) for all sufficiently large values of r 1, r 2,..., r n that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn ρ h (f) + ε) }] 1 M f (r 1, r 2,..., r n ) 1 vn ρ h (f) + ε) } ( vn λ h (g) ε)
6 138 Datta, Biswas, Dutta 1 M f (r 1, r 2,..., r n ) ( ρ h (f) + ε) ( vn λ h (g) ε) log (r 1r 2...r n ) log Since ε (> 0) is arbitrary, we obtain that ( ρ h (f) + ε) ( vn λ h (g) ε). 1 M f (r 1, r 2,..., r n ) ρ r 1,r 2 λ h (g) ρ vn ρ g (f) λ h (g). (2.11) Again from (2.2) in view of (2.5), we get for all sufficiently large values of r 1, r 2,..., r n that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn λ h (f) ε) }] 1 M f (r 1, r 2,..., r n ) 1 vn λ h (f) ε) } ( vn + ε) 1 M f (r 1, r 2,..., r n ) ( λ h (f) ε) ( vn + ε) log (r 1r 2...r n ) log ( λ h (f) ε) ( vn + ε). As ε (> 0) is arbitrary, it follows from above that 1 M f (r 1, r 2,..., r n ) λ lim inf r 1,r 2 λ vn λ g (f). (2.12) Also in view of (2.7), we get from (2.1) for a sequence of values of r 1, r 2,..., r n tending to infinity that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn ρ h (f) + ε) }] 1 M f (r 1, r 2,..., r n ) 1 vn ρ h (f) + ε) } ( vn ε) 1 M f (r 1, r 2,..., r n ) ( ρ h (f) + ε) ( vn ε) log (r 1r 2...r n ) log ( ρ h (f) + ε) ( vn ε).
7 Some inequalities in connection to relative orders... 7 (2016) No. 2, Since ε (> 0) is arbitrary, we get from above that 1 M f (r 1, r 2,..., r n ) ρ lim inf r 1,r 2 ρ vn λ g (f). (2.13) Similarly from (2.4) in view of (2.6), it follows for a sequence of values of r 1, r 2,..., r n tending to infinity that 1 M f (r 1, r 2,..., r n ) 1 M h {( vn λ h (f) + ε) }] 1 M f (r 1, r 2,..., r n ) 1 vn λ h (f) + ε) } ( vn λ h (g) ε) 1 M f (r 1, r 2,..., r n ) ( λ h (f) + ε) ( vn λ h (g) ε) log (r 1r 2...r n ) log ( λ h (f) + ε) ( vn λ h (g) ε). As ε (> 0) is arbitrary, we obtain from above that 1 M f (r 1, r 2,..., r n ) λ lim inf r 1,r 2 log (r 1 r 2r1 r 2...r n ) λ h (g) λ vn λ g (f) λ h (g). (2.14) Thus the theorem follows from (2.9), (2.10), (2.11), (2.12), (2.13) (2.14). In view of Theorem 2.1, one can easily verify the following corollaries: Corollary 2.2. Let f be an entire function of several complex variables with regular relative growth with respect to an entire function h of several complex variables g be entire another entire function of several complex variables. Then λ g (f) = vn ρ h (f) In addition, if vn ρ h (f) = vn, then λ g (f) = vn ρ f (g) = 1. vn ρ g (f) = vn ρ h (f) λ h (g). Corollary 2.3. Let f, g, h be three entire functions of several complex variables such that g is of regular relative growth with respect to an entire function h. Then λ g (f) = vn λ h (f) In addition, if vn ρ h (f) = vn then ρ g (f) = vn λ f (g) = 1. vn ρ g (f) = vn ρ h (f).
8 140 Datta, Biswas, Dutta Corollary 2.4. Let f g be any two entire functions of several complex variables with regular relative growth with respect to another entire function h of several complex variables respectively. Then λ g (f) = vn ρ g (f) = vn ρ h (f). Corollary 2.5. Let f g be any two entire functions of several complex variables with regular relative growth regular relative growth with respect to another entire function h of several complex variables respectively. Also suppose that vn ρ h (f) = vn. Then λ g (f) = vn ρ g (f) = vn λ f (g) = vn ρ f (g) = 1. Corollary 2.6. Let f, g h be any three entire functions of several complex variables such that either f is not of regular relative growth or g is not of regular relative growth with respect to h. Then ρ g (f) vn ρ f (g) 1 when f g are both of regular relative growth with respect to h respectively, then ρ g (f) vn ρ f (g) = 1. Corollary 2.7. Let f, g h be any three entire functions of several complex variables such that either f is not of regular relative growth or g is not of regular relative growth with respect to h. Then λ g (f) vn λ f (g) 1. when f g are both of regular relative growth with respect to h respectively, then λ g (f) vn λ f (g) = 1. Corollary 2.8. Let f g be any two entire functions of several complex variables. Then (i) vn λ g (f) = when vn = 0, (ii) vn ρ g (f) = when vn λ h (g) = 0, (iii) vn λ g (f) = 0 when vn = (iv) vn ρ g (f) = 0 when vn λ h (g) =. Corollary 2.9. Let f g be any two entire functions of several complex variables. Then (i) vn ρ g (f) = 0 when vn ρ h (f) = 0, (ii) vn λ g (f) = 0 when vn λ h (f) = 0, (iii) vn ρ g (f) = when vn ρ h (f) = (iv) vn λ g (f) = when vn λ h (f) =. Acknowledgment The authors are thankful to the referees for their valuable suggestions which have considerably improved the paper.
9 Some inequalities in connection to relative orders... 7 (2016) No. 2, References [1] A.K. Agarwal, On the properties of entire function of two complex variables, Canadian J. Math. 20 (1968) [2] L. Bernal, Crecimiento relativo de funciones enteras. Contribuci ón al estudio de lasfunciones enteras con índice exponencial finito, Doctoral Dissertation, University of Seville, Spain, [3] L. Bernal, Orden relativo de crecimiento de funciones enteras, Collect. Math. 39 (1988) [4] D. Banerjee R.K. Dutta, Relative order of entire functions of two complex variables, International J. of Math. Sci. & Engg. Appls. (IJMSEA) 1 (2007) [5] B.C. Chakraborty C. Roy, Relative order of an entire function, J. Pure Math. 23 (2006) [6] R.K. Dutta, Relative order of entire functions of several complex variables, Matematiqki Vesnik 65 (2013) [7] A.B. Fuks, Theory of analytic functions of several complex variables, Moscow, [8] M. Gil, Coupled systems of equations with entire polynomial functions, Int. J. Nonlinear Anal. Appl. 3 (2012) [9] S. Halvarsson, Growth properties of entire functions depending on a parameter, Annales Polonici Mathematici 14 (1996) [10] C.O. Kiselman, Order type as measure of growth for convex or entire functions, Proc. Lond. Math. Soc. 66 (1993) [11] C.O. Kiselman, Plurisubharmonic functions potential theory in several complex variable, a contribution to the book project, Development of Mathematics, , edited by Hean-Paul Pier. [12] B.K. Lahiri D. Banerjee, A note on relative order of entire functions, Bull. Cal. Math. Soc. 97 (2005) [13] C. Roy, On the relative order lower relative order of an entire function, Bull. Cal. Math. Soc. 102 (2010) [14] E.C. Titchmarsh, The theory of functions, 2nd ed., Oxford University Press, Oxford, 1968.
GROWTH ANALYSIS OF ENTIRE FUNCTIONS OF TWO COMPLEX VARIABLES
Sa Communications in Matematical Analysis (SCMA Vol. 3 No. 2 (2016 13-24 ttp://scma.marae.ac.ir GROWTH ANALYSIS OF ENTIRE FUNCTIONS OF TWO COMPLEX VARIABLES SANJIB KUMAR DATTA 1 AND TANMAY BISWAS 2 Abstract.
More informationRelative P-th Order of Entire Functions of Two Complex Variables
Relative P-th Order of Entire Functions of Two Complex Variables Ratan Kumar Dutta, Nintu Mal Abstract In this paper we introduce the idea of relative p-th order of entire functions of two complex variables.
More informationGROWTH PROPERTIES OF COMPOSITE ANALYTIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES IN UNIT POLYDISC FROM THE VIEW POINT OF THEIR NEVANLINNA L -ORDERS
Palestine Journal o Mathematics Vol 8209 346 352 Palestine Polytechnic University-PPU 209 GROWTH PROPERTIES OF COMPOSITE ANALYTIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES IN UNIT POLYDISC FROM THE VIEW POINT
More informationDerivation of Some Results on the Generalized Relative Orders of Meromorphic Functions
DOI: 10.1515/awutm-2017-0004 Analele Universităţii de Vest, Timişoara Seria Matematică Inormatică LV, 1, 2017), 51 61 Derivation o Some Results on te Generalized Relative Orders o Meromorpic Functions
More informationSome Results on the Growth Analysis of Entire Functions Using their Maximum Terms and Relative L -orders
Journal of Matematical Extension Vol. 10, No. 2, (2016), 59-73 ISSN: 1735-8299 URL: ttp://www.ijmex.com Some Results on te Growt Analysis of Entire Functions Using teir Maximum Terms and Relative L -orders
More informationA Special Type Of Differential Polynomial And Its Comparative Growth Properties
Sanjib Kumar Datta 1, Ritam Biswas 2 1 Department of Mathematics, University of Kalyani, Kalyani, Dist- Nadia, PIN- 741235, West Bengal, India 2 Murshidabad College of Engineering Technology, Banjetia,
More informationStudy of Growth Properties on the the Basis of Gol dberg Order of Composite Entire Functions of Several Variables
Int. Journal of Math. Analysis, Vol. 5, 2011, no. 23, 1139-1153 Study of Growth Properties on the the Basis of Gol dberg Order of Composite Entire Functions of Several Variables Sanjib Kumar atta epartment
More informationSome Results on the Growth Properties of Entire Functions Satifying Second Order Linear Differential Equations
Int Journal of Math Analysis, Vol 3, 2009, no 1, 1-14 Some Results on the Growth Properties of Entire Functions Satifying Second Order Linear Differential Equations Sanjib Kumar Datta Department of Mathematics,
More information1 Introduction, Definitions and Notations
Acta Universitatis Apulensis ISSN: 1582-5329 No 34/2013 pp 81-97 THE GROWTH ESTIMATE OF ITERATED ENTIRE FUNCTIONS Ratan Kumar Dutta Abstract In this paper we study growth properties of iterated entire
More informationSlowly Changing Function Oriented Growth Analysis of Differential Monomials and Differential Polynomials
Slowly Chanin Function Oriented Growth Analysis o Dierential Monomials Dierential Polynomials SANJIB KUMAR DATTA Department o Mathematics University o kalyani Kalyani Dist-NadiaPIN- 7235 West Benal India
More informationOn the Weak Type of Meromorphic Functions
International Mathematical Forum, 4, 2009, no 12, 569-579 On the Weak Type of Meromorphic Functions Sanjib Kumar Datta Department of Mathematics University of North Bengal PIN: 734013, West Bengal, India
More informationSome Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces
Mathematica Moravica Vol. 17-1 (013) 5 37 Some Fixed Point Theorems for Certain Contractive Mappings in G-Metric Spaces Amit Singh B. Fisher and R.C. Dimri Abstract. In this paper we prove some fixed point
More informationOn the mean values of an analytic function
ANNALES POLONICI MATHEMATICI LVII.2 (1992) On the mean values of an analytic function by G. S. Srivastava and Sunita Rani (Roorkee) Abstract. Let f(z), z = re iθ, be analytic in the finite disc z < R.
More informationWEIGHTED SHARING AND UNIQUENESS OF CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS
Palestine Journal of Mathematics Vol. 7(1)(2018), 121 130 Palestine Polytechnic University-PPU 2018 WEIGHTED SHARING AND UNIQUENESS OF CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS Pulak Sahoo and
More informationUNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING THREE VALUES
Kragujevac Journal of Mathematics Volume 38(1) (2014), Pages 105 123. UNIQUENESS OF MEROMORPHIC FUNCTIONS SHARING THREE VALUES ARINDAM SARKAR 1 AND PAULOMI CHATTOPADHYAY 2 Abstract. We prove four uniqueness
More information1 Introduction, Definitions and Results
Novi Sad J. Math. Vol. 46, No. 2, 2016, 33-44 VALUE DISTRIBUTION AND UNIQUENESS OF q-shift DIFFERENCE POLYNOMIALS 1 Pulak Sahoo 2 and Gurudas Biswas 3 Abstract In this paper, we deal with the distribution
More informationON WEAK AND STRONG CONVERGENCE THEOREMS FOR TWO NONEXPANSIVE MAPPINGS IN BANACH SPACES. Pankaj Kumar Jhade and A. S. Saluja
MATEMATIQKI VESNIK 66, 1 (2014), 1 8 March 2014 originalni nauqni rad research paper ON WEAK AND STRONG CONVERGENCE THEOREMS FOR TWO NONEXPANSIVE MAPPINGS IN BANACH SPACES Pankaj Kumar Jhade and A. S.
More informationA Fixed Point Theorem of Caccioppoli - Kannan Type on a Class of Generalized Metric Spaces
International Mathematical Forum, Vol. 9, 2014, no. 28, 1357-1361 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.4227 A Fixed Point Theorem of Caccioppoli - Kannan Type on a Class of
More informationWeak and Strong Convergence Theorems for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Nonself-Mappings
Int. J. Nonlinear Anal. Appl. 3 (2012) No. 1, 9-16 ISSN: 2008-6822 (electronic) http://www.ijnaa.semnan.ac.ir Weak and Strong Convergence Theorems for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive
More informationCONVERGENCE OF THE STEEPEST DESCENT METHOD FOR ACCRETIVE OPERATORS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 12, Pages 3677 3683 S 0002-9939(99)04975-8 Article electronically published on May 11, 1999 CONVERGENCE OF THE STEEPEST DESCENT METHOD
More informationAPPROXIMATION AND GENERALIZED LOWER ORDER OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES. Susheel Kumar and G. S. Srivastava (Received June, 2013)
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 45 (2015), 11 17 APPROXIMATION AND GENERALIZED LOWER ORDER OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES Susheel Kumar and G. S. Srivastava (Received June,
More informationCommon fixed point theorem for nonexpansive type single valued mappings
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 45-51 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.293 Common fixed point theorem for nonexpansive type single valued mappings Pankaj
More informationPolarization constant K(n, X) = 1 for entire functions of exponential type
Int. J. Nonlinear Anal. Appl. 6 (2015) No. 2, 35-45 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.252 Polarization constant K(n, X) = 1 for entire functions of exponential type A.
More informationApproximate additive and quadratic mappings in 2-Banach spaces and related topics
Int. J. Nonlinear Anal. Appl. 3 (0) No., 75-8 ISSN: 008-68 (electronic) http://www.ijnaa.semnan.ac.ir Approximate additive and quadratic mappings in -Banach spaces and related topics Y. J. Cho a, C. Park
More informationSecond Hankel determinant for the class of Bazilevic functions
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 3, 413 420 Second Hankel determinant for the class of Bazilevic functions D. Vamshee Krishna and T. RamReddy Abstract. The objective of this paper is to obtain
More informationRELATION BETWEEN SMALL FUNCTIONS WITH DIFFERENTIAL POLYNOMIALS GENERATED BY MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
Kragujevac Journal of Mathematics Volume 38(1) (2014), Pages 147 161. RELATION BETWEEN SMALL FUNCTIONS WITH DIFFERENTIAL POLYNOMIALS GENERATED BY MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL
More informationPICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 3(2017), Pages 42-51. PICARD OPERATORS IN b-metric SPACES VIA DIGRAPHS SUSHANTA KUMAR MOHANTA
More informationTwo-Step Iteration Scheme for Nonexpansive Mappings in Banach Space
Mathematica Moravica Vol. 19-1 (2015), 95 105 Two-Step Iteration Scheme for Nonexpansive Mappings in Banach Space M.R. Yadav Abstract. In this paper, we introduce a new two-step iteration process to approximate
More informationA generalization of Banach s contraction principle for nonlinear contraction in a partial metric space
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (01), 37 43 Research Article A generalization of Banach s contraction principle for nonlinear contraction in a partial metric space Wasfi Shatanawi
More informationON WEAK CONVERGENCE THEOREM FOR NONSELF I-QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
BULLETIN OF INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 69-75 Former BULLETIN OF SOCIETY OF MATHEMATICIANS BANJA LUKA ISSN 0354-5792 (o), ISSN 1986-521X (p) ON WEAK CONVERGENCE
More informationCommon Fixed Point Theorems for Six Mappings Satisfying Almost Generalized (S, T)-Contractive Condition in Partially Ordered Metric Spaces
Annals of Pure Applied Mathematics Vol. 1, No., 016, 143-151 ISSN: 79-087X (P), 79-0888(online) Published on 7 November 016 www.researchmathsci.org Annals of Common Fixed Point Theorems for Six Mappings
More informationDeficiency And Relative Deficiency Of E-Valued Meromorphic Functions
Applied Mathematics E-Notes, 323, -8 c ISSN 67-25 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Deficiency And Relative Deficiency Of E-Valued Meromorphic Functions Zhaojun Wu, Zuxing
More informationViscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces
Viscosity Iterative Approximating the Common Fixed Points of Non-expansive Semigroups in Banach Spaces YUAN-HENG WANG Zhejiang Normal University Department of Mathematics Yingbing Road 688, 321004 Jinhua
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics SOME NORMALITY CRITERIA INDRAJIT LAHIRI AND SHYAMALI DEWAN Department of Mathematics University of Kalyani West Bengal 741235, India. EMail: indrajit@cal2.vsnl.net.in
More informationHAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
Georgian Mathematical Journal Volume 9 (2002), Number 3, 591 600 NONEXPANSIVE MAPPINGS AND ITERATIVE METHODS IN UNIFORMLY CONVEX BANACH SPACES HAIYUN ZHOU, RAVI P. AGARWAL, YEOL JE CHO, AND YONG SOO KIM
More informationCommon fixed points for α-ψ-ϕ-contractions in generalized metric spaces
Nonlinear Analysis: Modelling and Control, 214, Vol. 19, No. 1, 43 54 43 Common fixed points for α-ψ-ϕ-contractions in generalized metric spaces Vincenzo La Rosa, Pasquale Vetro Università degli Studi
More informationFixed Point Theorems for -Monotone Maps on Partially Ordered S-Metric Spaces
Filomat 28:9 (2014), 1885 1898 DOI 10.2298/FIL1409885D Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Fixed Point Theorems for
More informationConvergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces
Mathematica Moravica Vol. 19-1 2015, 33 48 Convergence to Common Fixed Point for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense in Banach Spaces Gurucharan Singh Saluja Abstract.
More informationOn coupled generalised Banach and Kannan type contractions
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 5 (01, 59 70 Research Article On coupled generalised Banach Kannan type contractions B.S.Choudhury a,, Amaresh Kundu b a Department of Mathematics,
More informationCommon fixed point of multivalued graph contraction in metric spaces
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 225-230 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.309 Common fixed point of multivalued graph contraction in metric spaces Masoud
More informationSome fixed point theorems in G-metric spaces
Math. Sci. Lett. 1, No. 1, 25-31 (2012) 25 Mathematical Sciences Letters. An International Journal Some fixed point theorems in G-metric spaces Binayak S 1. Choudhury 1, Sanjay Kumar 2, Asha 3 and Krishnapada
More informationBulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp
Bulletin of the Iranian Mathematical Society Vol. 39 No.6 (2013), pp 1125-1135. COMMON FIXED POINTS OF A FINITE FAMILY OF MULTIVALUED QUASI-NONEXPANSIVE MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES A. BUNYAWAT
More informationCoincidence point results of multivalued weak C-contractions on metric spaces with a partial order
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 6 (2013), 7 17 Research Article Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order Binayak S. Choudhury
More informationCONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS. 1. Introduction
CONVERGENCE THEOREMS FOR MULTI-VALUED MAPPINGS YEKINI SHEHU, G. C. UGWUNNADI Abstract. In this paper, we introduce a new iterative process to approximate a common fixed point of an infinite family of multi-valued
More informationDifferential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients
Differential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients Waggas Galib Atshan and Ali Hamza Abada Department of Mathematics College of Computer Science and Mathematics
More informationON STRONGLY PRE-OPEN SETS AND A DECOMPOSITION OF CONTINUITY. Chandan Chattopadhyay
MATEMATIQKI VESNIK 57 (2005), 121 125 UDK 515.122.2 originalni nauqni rad research paper ON STRONGLY PRE-OPEN SETS AND A DECOMPOSITION OF CONTINUITY Chandan Chattopadhyay Abstract. In this paper some new
More informationA note on a Soft Topological Space
Punjab University Journal of Mathematics (ISSN 1016-2526) Vol. 46(1) (2014) pp. 19-24 A note on a Soft Topological Space Sanjay Roy Department of Mathematics South Bantra Ramkrishna Institution Howrah,
More informationCOMMON FIXED POINTS IN b-metric SPACES ENDOWED WITH A GRAPH. Sushanta Kumar Mohanta. 1. Introduction
MATEMATIQKI VESNIK 68, 2 (2016), 140 154 June 2016 originalni nauqni rad research paper COMMON FIXED POINTS IN b-metric SPACES ENDOWED WITH A GRAPH Sushanta Kumar Mohanta Abstract. We discuss the existence
More informationAPPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS. G. S. Srivastava and Susheel Kumar
ARCHIVUM MATHEMATICUM BRNO) Tomus 45 2009), 137 146 APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS G. S. Srivastava and Susheel Kumar Abstract. In the present paper, we study the polynomial
More informationVALUE DISTRIBUTION OF THE PRODUCT OF A MEROMORPHIC FUNCTION AND ITS DERIVATIVE. Abstract
I. LAHIRI AND S. DEWAN KODAI MATH. J. 26 (2003), 95 100 VALUE DISTRIBUTION OF THE PRODUCT OF A MEROMORPHIC FUNCTION AND ITS DERIVATIVE Indrajit Lahiri and Shyamali Dewan* Abstract In the paper we discuss
More informationON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 3, 2018 ISSN 1223-7027 ON A HYBRID PROXIMAL POINT ALGORITHM IN BANACH SPACES Vahid Dadashi 1 In this paper, we introduce a hybrid projection algorithm for a countable
More informationOn a functional equation connected with bi-linear mappings and its Hyers-Ulam stability
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 017, 5914 591 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa On a functional equation connected
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics ON SOME APPROXIMATE FUNCTIONAL RELATIONS STEMMING FROM ORTHOGONALITY PRESERVING PROPERTY JACEK CHMIELIŃSKI Instytut Matematyki, Akademia Pedagogiczna
More informationJordan Journal of Mathematics and Statistics (JJMS) 11(1), 2018, pp I-CONVERGENCE CLASSES OF SEQUENCES AND NETS IN TOPOLOGICAL SPACES
Jordan Journal of Mathematics and Statistics (JJMS) 11(1), 2018, pp 13-31 I-CONVERGENCE CLASSES OF SEQUENCES AND NETS IN TOPOLOGICAL SPACES AMAR KUMAR BANERJEE (1) AND APURBA BANERJEE (2) Abstract. In
More informationEXISTENCE RESULTS FOR QUASILINEAR HEMIVARIATIONAL INEQUALITIES AT RESONANCE. Leszek Gasiński
DISCRETE AND CONTINUOUS Website: www.aimsciences.org DYNAMICAL SYSTEMS SUPPLEMENT 2007 pp. 409 418 EXISTENCE RESULTS FOR QUASILINEAR HEMIVARIATIONAL INEQUALITIES AT RESONANCE Leszek Gasiński Jagiellonian
More informationWEAK CONVERGENCE OF RESOLVENTS OF MAXIMAL MONOTONE OPERATORS AND MOSCO CONVERGENCE
Fixed Point Theory, Volume 6, No. 1, 2005, 59-69 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm WEAK CONVERGENCE OF RESOLVENTS OF MAXIMAL MONOTONE OPERATORS AND MOSCO CONVERGENCE YASUNORI KIMURA Department
More informationNew Coupled Common Fixed Point for Four Mappings satisfying Rational Contractive Expression
New Coupled Common Fixed Point for Four Mappings satisfying Rational Contractive Expression H K Nashine 1, A Gupta 2 1 Department of Mathematics, Amity University, Manth Kharora, Raipur-(Chhattisgarh),
More informationBohr property of bases in the space of entire functions and its generalizations
Submitted exclusively to the London Mathematical Society doi:.2// Bohr property of bases in the space of entire functions and its generalizations Aydin Aytuna and Plamen Djakov Dedicated to Tosun Terzioğlu
More informationEpiconvergence and ε-subgradients of Convex Functions
Journal of Convex Analysis Volume 1 (1994), No.1, 87 100 Epiconvergence and ε-subgradients of Convex Functions Andrei Verona Department of Mathematics, California State University Los Angeles, CA 90032,
More informationBulletin of the. Iranian Mathematical Society
ISSN: 7-6X Print) ISSN: 735-855 Online) Bulletin of the Iranian Mathematical Society Vol 4 6), No, pp 95 Title: A note on lacunary series in Q K spaces Authors): J Zhou Published by Iranian Mathematical
More informationOn a new class of (j, i)-symmetric function on conic regions
Available online at wwwisr-publicationscom/jnsa J Nonlinear Sci Appl 10 (2017) 4628 4637 Research Article Journal Homepage: wwwtjnsacom - wwwisr-publicationscom/jnsa On a new class of (j i)-symmetric function
More informationFIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES. 1. Introduction and preliminaries
Asia Pacific Journal of Mathematics, Vol. 1, No. 1 (2014), 67-85 ISSN 2357-2205 FIXED POINT AND COMMON FIXED POINT THEOREMS IN CONE BALL-METRIC SPACES ANIMESH GUPTA Department of Applied Mathematics, Vidhyapeeth
More informationInvariant Approximation Results of Generalized Contractive Mappings
Filomat 30:14 (016), 3875 3883 DOI 10.98/FIL1614875C Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Invariant Approximation Results
More informationL p -convergence of Bernstein Kantorovich-type operators. by Michele Campiti (Bari) and Giorgio Metafune (Lecce)
ANNALES POLONICI MATHEMATICI LXIII.3 (996) L p -convergence of Bernstein Kantorovich-type operators by Michele Campiti (Bari) and Giorgio Metafune (Lecce) Abstract. We study a Kantorovich-type modification
More informationTHE SEMI ORLICZ SPACE cs d 1
Kragujevac Journal of Mathematics Volume 36 Number 2 (2012), Pages 269 276. THE SEMI ORLICZ SPACE cs d 1 N. SUBRAMANIAN 1, B. C. TRIPATHY 2, AND C. MURUGESAN 3 Abstract. Let Γ denote the space of all entire
More informationFixed point of ϕ-contraction in metric spaces endowed with a graph
Annals of the University of Craiova, Mathematics and Computer Science Series Volume 374, 2010, Pages 85 92 ISSN: 1223-6934 Fixed point of ϕ-contraction in metric spaces endowed with a graph Florin Bojor
More informationSang-baek Lee*, Jae-hyeong Bae**, and Won-gil Park***
JOURNAL OF THE CHUNGCHEONG MATHEMATICAL SOCIETY Volume 6, No. 4, November 013 http://d.doi.org/10.14403/jcms.013.6.4.671 ON THE HYERS-ULAM STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY Sang-baek Lee*,
More informationA FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS
Fixed Point Theory, (0), No., 4-46 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html A FIXED POINT THEOREM FOR GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS A. ABKAR AND M. ESLAMIAN Department of Mathematics,
More informationFixed Point Theorems for Mapping Having The Mixed Monotone Property
International Archive of Applied Sciences and Technology Int. Arch. App. Sci. Technol; Vol 5 [2]June 2014: 19-23 2014 Society of Education India [ISO9001: 2008 Certified Organization] www.soeagra.co/iaast.html
More informationFixed point results and an application to homotopy in modular metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 8 (015), 900 908 Research Article Fixed point results and an application to homotopy in modular metric spaces Meltem Erden Ege a, Cihangir Alaca
More informationWeak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings
Mathematica Moravica Vol. 20:1 (2016), 125 144 Weak and strong convergence theorems of modified SP-iterations for generalized asymptotically quasi-nonexpansive mappings G.S. Saluja Abstract. The aim of
More informationExtremal I-Limit Points Of Double Sequences
Applied Mathematics E-Notes, 8(2008), 131-137 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Extremal I-Limit Points Of Double Sequences Mehmet Gürdal, Ahmet Şahiner
More informationSubordination and Superordination Results for Analytic Functions Associated With Convolution Structure
Int. J. Open Problems Complex Analysis, Vol. 2, No. 2, July 2010 ISSN 2074-2827; Copyright c ICSRS Publication, 2010 www.i-csrs.org Subordination and Superordination Results for Analytic Functions Associated
More informationMEROMORPHIC FUNCTIONS AND ALSO THEIR FIRST TWO DERIVATIVES HAVE THE SAME ZEROS
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 30, 2005, 205 28 MEROMORPHIC FUNCTIONS AND ALSO THEIR FIRST TWO DERIVATIVES HAVE THE SAME ZEROS Lian-Zhong Yang Shandong University, School of Mathematics
More informationSOME GENERALIZATION OF MINTY S LEMMA. Doo-Young Jung
J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 6(1999), no 1. 33 37 SOME GENERALIZATION OF MINTY S LEMMA Doo-Young Jung Abstract. We obtain a generalization of Behera and Panda s result on nonlinear
More informationAPPROXIMATING SOLUTIONS FOR THE SYSTEM OF REFLEXIVE BANACH SPACE
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 2 Issue 3(2010), Pages 32-39. APPROXIMATING SOLUTIONS FOR THE SYSTEM OF φ-strongly ACCRETIVE OPERATOR
More informationOn the decay of elements of inverse triangular Toeplitz matrix
On the decay of elements of inverse triangular Toeplitz matrix Neville Ford, D. V. Savostyanov, N. L. Zamarashkin August 03, 203 arxiv:308.0724v [math.na] 3 Aug 203 Abstract We consider half-infinite triangular
More informationA Note on the Generalized Shift Map
Gen. Math. Notes, Vol. 1, No. 2, December 2010, pp. 159-165 ISSN 2219-7184; Copyright c ICSRS Publication, 2010 www.i-csrs.org Available free online at http://www.geman.in A Note on the Generalized Shift
More informationGeneralized Monotonicities and Its Applications to the System of General Variational Inequalities
Generalized Monotonicities and Its Applications to the System of General Variational Inequalities Khushbu 1, Zubair Khan 2 Research Scholar, Department of Mathematics, Integral University, Lucknow, Uttar
More informationCOMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE
Kragujevac Journal of Mathematics Volume 35 Number 3 (2011), Pages 463 470. COMMON FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE B. D. PANT, SUNNY CHAUHAN AND QAMAR ALAM Abstract. The notion of weakly
More informationIN PROBABILITY. Kragujevac Journal of Mathematics Volume 42(1) (2018), Pages
Kragujevac Journal of Mathematics Volume 4) 08), Pages 5 67. A NOTION OF -STATISTICAL CONVERGENCE OF ORDER γ IN PROBABILITY PRATULANANDA DAS, SUMIT SOM, SANJOY GHOSAL, AND VATAN KARAKAYA 3 Abstract. A
More informationASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN MODULAR FUNCTION SPACES ABSTRACT
ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN MODULAR FUNCTION SPACES T. DOMINGUEZ-BENAVIDES, M.A. KHAMSI AND S. SAMADI ABSTRACT In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying
More informationV. Popa, A.-M. Patriciu ( Vasile Alecsandri Univ. Bacău, Romania)
UDC 51791 V Popa, A-M Patriciu ( Vasile Alecsandri Univ Bacău, Romania) FIXED-POINT RESULTS ON COMPLETE G-METRIC SPACES FOR MAPPINGS SATISFYING AN IMPLICIT RELATION OF A NEW TYPE РЕЗУЛЬТАТИ ПРО НЕРУХОМУ
More informationUniformly convex functions II
ANNALES POLONICI MATHEMATICI LVIII. (199 Uniformly convex functions II by Wancang Ma and David Minda (Cincinnati, Ohio Abstract. Recently, A. W. Goodman introduced the class UCV of normalized uniformly
More informationBulletin of the. Iranian Mathematical Society
ISSN: 1017-060X (Print) ISSN: 1735-8515 (Online) Bulletin of the Iranian Mathematical Society Vol. 41 (2015), No. 5, pp. 1259 1269. Title: A uniform approximation method to solve absolute value equation
More informationTwo-dimensional examples of rank-one convex functions that are not quasiconvex
ANNALES POLONICI MATHEMATICI LXXIII.3(2) Two-dimensional examples of rank-one convex functions that are not quasiconvex bym.k.benaouda (Lille) andj.j.telega (Warszawa) Abstract. The aim of this note is
More informationAdomian decomposition method for fuzzy differential equations with linear differential operator
ISSN 1746-7659 England UK Journal of Information and Computing Science Vol 11 No 4 2016 pp243-250 Adomian decomposition method for fuzzy differential equations with linear differential operator Suvankar
More informationFixed Point Theorems in Vector Metric Spaces
Int. Journal of Math. Analysis, Vol. 4, 2010, no. 48, 2395-2400 Fixed Point Theorems in Vector Metric Spaces Lakshmi Kanta Dey Department of Mathematics National Institute of Technology Durgapur, Durgapur-713
More informationCONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
International Journal of Analysis and Applications ISSN 2291-8639 Volume 8, Number 1 2015), 69-78 http://www.etamaths.com CONVERGENCE OF HYBRID FIXED POINT FOR A PAIR OF NONLINEAR MAPPINGS IN BANACH SPACES
More informationConvergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 2016), 5119 5135 Research Article Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense Gurucharan
More informationBest proximity point results in set-valued analysis
Nonlinear Analysis: Modelling and Control, Vol. 21, No. 3, 293 305 ISSN 1392-5113 http://dx.doi.org/10.15388/na.2016.3.1 Best proximity point results in set-valued analysis Binayak S. Choudhury a, Pranati
More informationCONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES. Jong Soo Jung. 1. Introduction
Korean J. Math. 16 (2008), No. 2, pp. 215 231 CONVERGENCE OF APPROXIMATING FIXED POINTS FOR MULTIVALUED NONSELF-MAPPINGS IN BANACH SPACES Jong Soo Jung Abstract. Let E be a uniformly convex Banach space
More informationA fixed point theorem on compact metric space using hybrid generalized ϕ - weak contraction
Theoretical Mathematics & Applications, vol. 4, no. 4, 04, 9-8 ISSN: 79-9687 (print), 79-9709 (online) Scienpress Ltd, 04 A fixed point theorem on compact metric space using hybrid generalized ϕ - weak
More informationSECOND ORDER DUALITY IN MULTIOBJECTIVE PROGRAMMING
Journal of Applied Analysis Vol. 4, No. (2008), pp. 3-48 SECOND ORDER DUALITY IN MULTIOBJECTIVE PROGRAMMING I. AHMAD and Z. HUSAIN Received November 0, 2006 and, in revised form, November 6, 2007 Abstract.
More informationCertain classes of p-valent analytic functions with negative coefficients and (λ, p)-starlike with respect to certain points
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 379), 2015, Pages 35 49 ISSN 1024 7696 Certain classes of p-valent analytic functions with negative coefficients and λ, p)-starlike
More informationCESÁRO TYPE OPERATORS ON SPACES OF ANALYTIC FUNCTIONS. S. Naik
Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 25:4 2, 85 97 DOI:.2298/FIL485N CESÁRO TYPE OPERATORS ON SPACES OF ANALYTIC FUNCTIONS
More informationCONTROLLABILITY OF NONLINEAR DISCRETE SYSTEMS
Int. J. Appl. Math. Comput. Sci., 2002, Vol.2, No.2, 73 80 CONTROLLABILITY OF NONLINEAR DISCRETE SYSTEMS JERZY KLAMKA Institute of Automatic Control, Silesian University of Technology ul. Akademicka 6,
More information1. Introduction EKREM SAVAŞ
Matematiqki Bilten ISSN 035-336X Vol.39 (LXV) No.2 205 (9 28) UDC:55.65:[57.52:59.222 Skopje, Makedonija I θ -STATISTICALLY CONVERGENT SEQUENCES IN TOPOLOGICAL GROUPS EKREM SAVAŞ Abstract. Recently, Das,
More informationA Common Fixed Point Result in Complex Valued b-metric Spaces under Contractive Condition
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 4869-4876 Research India Publications http://www.ripublication.com A Common Fixed Point Result in Complex
More informationSOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH EXCEPTIONALLY FEW ZEROS
Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 23, 1998, 429 452 SOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH EXCEPTIONALLY FEW ZEROS Gary G. Gundersen, Enid M. Steinbart, and
More information