j(z) > + FZ f(z) z + oz f(z) 1-.F < 1-.F zf (z) } 1 E (z 6 U,F 1). (1.3) >/(z e u) ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS
|
|
- Lambert Fleming
- 5 years ago
- Views:
Transcription
1 Internat. J. Math. & Math. Sci. VOL. 1 NO. (1998) ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS NAK EUN CHO, IN HWA KIM JI A KIM Department of Applied Mathematics Pukyong National University Pusan , KOREA (Received April 1, 1996 in revised form September 30, 1996) ABSTRACT. The object of the present paper is to derive some ument properties of certain integral operators. Our results contain some interesting corollaries as the special cases. KEY WORDS AND PHRASES: Argument, integral operators, starlike functions, Bazilevi6 functions AMS SUBJECT CLASSHICATION CODES: 30C INTRODUCTION Let A denote the class offunctions ofthe form f(z) z + oz subordinate to g, written f g, if there exists a Schwarz function w(z) in U such that f(z) A function f e A is said to be in the class S* [E, F] if zf (z) l+ez < (z6u,i<f<e<i) f() which are analytic in the open unit disk U { z Iz < 1}. If f g are analytic in U, we say that f is + FZ g(w(z)). The class S*[E,F] was studied in [1,]. In particular, S [1 c, 1] S (c)(0 _< c < 1) is the well known class of starlike functions of order a. We observe [] that a function f is in S"[E,F] if only if f(z) 1.F < 1.F Re zf (z) } 1 E (z 6 U,F 1). (1.3) j(z) > A function f e A is said to be in the class B(p, a, ) if it satisfies Re{ } Zf (z)f"i g,,() >/(z e u) for some #(# > 0), (0 _< < I) g e S*(o). Furthermore, we denote BI(/, a,/) bythe subclass of B(/, a,,o) for g(z) =_ z e S* (a). The classes B(, a,/) B (/, a, ) are the subclasses of Bazilevi6 functions in U [3]. We also note that B(I, a,/) C(a,/) is an important subclass of closetoconvex functions [4]. For a positive real number # > 0 a function f A, we define the integral operator Jc., by
2 370 N.E. CliO, I. H KIM AND J. A KIM Jcu(f) c + # tcl fu(t)dt ;(c > (1 4) Kumar Shukla [5] showed that the integral operator Jc,u(f) defined by (1.4) belongs to the class S*[E,F] for c >_ u(g:l)l_f, whenever f S [E,F]. The operator Je.1, when c N {1,,3,.}, was introduced by Bemardi [6]. Further, the operator J. was studied earlier by Libera [7] Livingston [8]. In the present paper, we give some ument properties of the integral operator defined by (1.4). We also generalize the previous results of Libera [7], Owa Srivastava [9] Owa Obradovi6 10].. MAIN RESULTS In proving our main results, we shall need the following lemmas. LEMMA 1 ([11]). Let M(z) N(z) be regular in U with M(0) N(0) 0, let/ be real. If N(z) maps U onto a (possibly manysheeted) region which is starlike with respect to the origin, then Re N (z) > (z e U) = Re M(z) Re N.t{z) <,O(z U) = Re N( z) < (z U). LEMMA ([1]). Let p(z) be analytic in U, p(0) 1, p(z) :/:. 0 in U suppose that there exists a point zo U such that Iv()l < fo I1 < Iol / > 0. Then we have o (o) ik, whvn p(zo) r when k<1(1) a+a p(zo) p(o) + m( > o). With the help oflemma Lemma, we now derive THEOREM 1. Let c # be real numbers with c > 0, > 0 1 < F < E < 1 let.fa If
3 for some g S" [E, F], then < ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS 3 71 T(0_< <1,0<_<1) arc,. is the imegral operator defined by (1.4) r/(o < r/_< 1) is the solution ofthe equation when {(rsin(1t(e,f))) 7r c + +rlcos (1 tc(e,f)) 6 7+Tan 1 _ for F :/: 1 I+F r] " for F= 1, tc(e,f) 8in_ E F 7r ( c(1f)+ief M(z) p(z) N(z) 1 M(z) zf, (z) c tif"(t)dt t1 tctg(t)dt PROOF. Let us put N(z) # tc gu(t)dt. (.1) (.) Then p(z) is analytic in Uwith p(0) 1. By a simple calculation, we have zp (z)) M (z) N(z) p(z) 1 N (z) + zn (z) p(z) 1(zf (z)f"(z) ) Since g e S*[E,F], J.(g) e S*[E,F] [5] hence N(z) is (possibly manysheeted) starlike function with respect to the origin. Therefore, from our assumption Lemma 1, p(z) 0 in U. If there exists a point zo 6 U such that [v(z)[< for Izl < Izol then, from Lemma, we have 0p (o) when p(zo
4 37 N.E. CHO, I. H. KIM AND J. AK/M when p(zo) p(zo) i.(. > 0). Since Jc.z(g) E S [E,F], from (1.) (1.3), we have g () (&,(g)) / c pe T, N() J,.() 1E I+E c + I.F < P < C + tc(e,f)<<t(e,f) forf# I, when t,(e, F) is given by (.), 1E c+ <p< oo, 1<<1 for F= 1. At first, suppose that p(zo) ia(a > 0). For the case F : 1, we obtain z0f (z0)f"i (z0) _/) (1 )M (zo) N (zo) ( 1 p(zo) z(y.,.(g)) &(g) + c p(zo) rr7 + ()1 + (pe ],, irlk + zo/g(z,o)) Tan1 g +o g( ) _> r?" / Tan_ ( sin (1 tc(e,f)) c / +EI+F +cos (1. t(e,f)) _r_, t(e,f) 6 are given by (.) (.1), respectively. Similarly, for the case F 1, we have (f()f() ) These are a contradiction to the assumption of our theorem. Next, suppose that p(zo) ia(a > 0). For the case F 4= 1, applying the same method as the above, we have (zf (z)fz(z) < Tan_ nsin(1t(e,f)) "Tr ( [ I+EI+F /7]C08 "(1 t(e,f) 6 are given by (.) (.1), respectively for the case F 1, we have
5 ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS 373 / ()/" () g"(zo) B ) < which are contradictions to the assumption. Therefore we complete the proof of our theorem. Taking E 1 a(0 < a < 1) F 1 in Theorem 1, we have COROLLARY 1. Let c _> 0, # > 0 f E A. If for some g E S* (a), then z f (z)f"(z) g(z) < (0 < < 1, 0 < < 1) dc,u is the imegral operator defined by (1.4). REMARK 1. For 6 1, Corollary is the result obtained by Owa Obradovi6 [10]. Setting E 1, F 1, 1, 6 1 g(z) z in Theorem l, we have COROLLARY. Let c _> 0 f A. If then.re ft(z) >/(0 <_/5 < I), e (s,. (I)) >/, Jc,1 is the imegral operator defined by (1.4). Letting # 1 in Theorem 1, we have COROLLARY 3. Let c _> 0 1 _< F < E < 1 let f A. If for some g 6 S" [E, F], then g(z) )1 / <(0_</<1,0<6<1) Jc,1 is the integral operator defined by (1.4) r/(0 < r/< 1) is the solution ofthe equation (.1). Taking E 1 a(0 _< a < 1) F 1 in Corollary 3, we have COROLLARY 4. Let c >_ 0 f A. If then Jc, l(f) cz <, Jc,1 is the integral operator defined by (1.4). Putting E 1 a(0 _< a < 1), F 1 //= 1 in Corollary 3 Corollary 4, we obtain the following result of Owa Srivastava [9]. COROLLARY 5. If the function f defined by (1.1) is in the class C(c,/), then the integral operator Jc,1 (f)(c > 0) defined by (1.4) is also in the class c(a,/). REMARK. Taking c =/ 0 c 1 in Corollary 5, we obtain the result given earlier by Libera [7]
6 374 N.E. CliO, I. H. KIM AND J. AKIM By using the same technique as in proving Theorem 1, we have THEOREM. Let c # be real numbers with c > 0,/ > 0 1 < F < E < 1 let fa. If,qV(z) < (/ > 1, 0 < 6 <_ 1) for some g E S* [E, F], then Jc,, is the integral operator defined by (1.4) r/(0 < r/< 1) is the solution ofthe equation (.1) Putting g 1 a(0 < a < 1), F 1, # in Theorem, we have the following result by Owa Srivastava [9]. COROLLARY 6. Let c > 0.f E A. If () <(>1) for some g S* (c), then z(jc,1 (f)) },Jc,1 is the integral operator defined by (1.4). ACKNOWLEDGEMENT. The authors would like to thank Professor M. Nunokawa for his thought encouragement much valuable advice in the preparation of this paper. This work was partially supported by Non Directed Research Fund, Korea Research Foundation, 1996 the Basic Science Research Program, Ministry ofeducation, Project No. BSRI REFERENCES [l] JANOWSKI, W., Some extremal problems for certain families of analytic functions, Bull. de L Acad Pol. des ScL 1 (1973), 175. [] SILVERMAN, H. SILVIA, E.M, Subclasses of starlike functions subordinate to convex functions, Can. d. Math. 37 (1985), 4861 [3] SINGH, R., On Bazilevi functions, Proc. Amer. Math. Soc. l (195), 169,815. [4] KAPLAN, W., Closetoconvex Schlicht functions, Michigan Math. 1 (195), [5] KUMAR, V. SHUKLA, S.L., On pvalent starlike functions with reference to the Bemardi integral operator, Bull. Austral. Math. Soc. 30 (1984), [6] BERNARDI, S.D., Convex starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), [7] LIBERA, R.J., Some classes of regular univalent functions, Proc. Amer. Math. Soc. 16 (1965), [8] LIVINGSTIN, A.E., On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 17 (1966), [9] OWA, S. SRIVASTAVA, H.M., Some applications of the generalized Libera imegral operator, Proc. Japan Acad 6, Ser. A (1986), [10] OWA, S. OBRADOVI(, M., Certain subclasses of Bazilevi/: functions of type c, Internat. d. Math. Math. ScL 9 (1986), ] MILLER, S.S. MOCANU, P.T., Second order differemial inequalities in the complex plane, o Math. Anal. AppL 65 (1978), ] NUNOKAWA, M., On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad 69, Set. A (1993), 3437.
7 Advances in Operations Research Volume 014 Advances in Decision Sciences Volume 014 Applied Mathematics Algebra Volume 014 Probability Statistics Volume 014 The Scientific World Journal Volume 014 International Differential Equations Volume 014 Volume 014 Submit your manuscripts at International Advances in Combinatorics Mathematical Physics Volume 014 Complex Analysis Volume 014 International Mathematics Mathematical Sciences Mathematical Problems in Engineering Mathematics Volume 014 Volume 014 Volume 014 Volume 014 Discrete Mathematics Volume 014 Discrete Dynamics in Nature Society Function Spaces Abstract Applied Analysis Volume 014 Volume 014 Volume 014 International Stochastic Analysis Optimization Volume 014 Volume 014
The Noor Integral and Strongly Starlike Functions
Journal of Mathematical Analysis and Applications 61, 441 447 (001) doi:10.1006/jmaa.001.7489, available online at http://www.idealibrary.com on The Noor Integral and Strongly Starlike Functions Jinlin
More informationOn differential subordinations in the complex plane
Nunokawa et al. Journal of Inequalities Applications 015) 015:7 DOI 10.1186/s13660-014-0536-9 R E S E A R C H Open Access On differential subordinations in the complex plane Mamoru Nunokawa 1, Nak Eun
More informationOn the improvement of Mocanu s conditions
Nunokawa et al. Journal of Inequalities Applications 13, 13:46 http://www.journalofinequalitiesapplications.com/content/13/1/46 R E S E A R C H Open Access On the improvement of Mocanu s conditions M Nunokawa
More informationSOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR. Maslina Darus and Imran Faisal
Acta Universitatis Apulensis ISSN: 1582-5329 No. 29/212 pp. 197-215 SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR Maslina Darus and Imran Faisal Abstract. Let A denote
More informationSufficient conditions for starlike functions associated with the lemniscate of Bernoulli
Kumar et al. Journal of Inequalities and Applications 2013, 2013:176 R E S E A R C H Open Access Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli S Sivaprasad Kumar
More informationarxiv: v1 [math.cv] 19 Jul 2012
arxiv:1207.4529v1 [math.cv] 19 Jul 2012 On the Radius Constants for Classes of Analytic Functions 1 ROSIHAN M. ALI, 2 NAVEEN KUMAR JAIN AND 3 V. RAVICHANDRAN 1,3 School of Mathematical Sciences, Universiti
More informationAN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS
AN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS SUKHWINDER SINGH SUSHMA GUPTA AND SUKHJIT SINGH Department of Applied Sciences Department of Mathematics B.B.S.B. Engineering
More informationSOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS
Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 7 (01), No. 3, pp. 43-436 SOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS DINGGONG YANG 1 AND NENG XU,b 1 Department
More informationSANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS
East Asian Mathematical Journal Vol. 28 (2012), No. 3, pp. 321 332 SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS Nak Eun Cho Abstract. The purpose of the
More informationCoecient bounds for certain subclasses of analytic functions of complex order
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1015 1022 Coecient bounds for certain subclasses of analytic functions of complex order Serap Bulut Abstract In this paper, we introduce
More informationAn Integrodifferential Operator for Meromorphic Functions Associated with the Hurwitz-Lerch Zeta Function
Filomat 30:7 (2016), 2045 2057 DOI 10.2298/FIL1607045A Pulished y Faculty of Sciences Mathematics, University of Niš, Seria Availale at: http://www.pmf.ni.ac.rs/filomat An Integrodifferential Operator
More informationSUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS
SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS, P.G. Student, Department of Mathematics,Science College, Salahaddin University, Erbil, Region of Kurdistan, Abstract: In
More informationInclusion and argument properties for certain subclasses of multivalent functions defined by the Dziok-Srivastava operator
Advances in Theoretical Alied Mathematics. ISSN 0973-4554 Volume 11, Number 4 016,. 361 37 Research India Publications htt://www.riublication.com/atam.htm Inclusion argument roerties for certain subclasses
More informationZ bz Z klak --bkl <-- 6 (12) Z bkzk lbl _< 6. Z akzk (ak _> O, n e N {1,2,3,...}) N,,,(e) g A(n) g(z)- z- > (z U) (2 l) f(z)
Internat. J. Math. & Math. Sci. VOL. 19 NO. 4 (1996) 797-800 797 NEIGHBORHOODS OF CERTAIN ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS OSMAN ALTINTAS Department of Mathematics Hacettepe University Beytepe,
More informationA NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 32010), Pages 109-121. A NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS S.
More informationConvolution properties for subclasses of meromorphic univalent functions of complex order. Teodor Bulboacă, Mohamed K. Aouf, Rabha M.
Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 26:1 (2012), 153 163 DOI: 10.2298/FIL1201153B Convolution properties for subclasses of meromorphic
More informationA general coefficient inequality 1
General Mathematics Vol. 17, No. 3 (2009), 99 104 A general coefficient inequality 1 Sukhwinder Singh, Sushma Gupta and Sukhjit Singh Abstract In the present note, we obtain a general coefficient inequality
More informationConvolution and Subordination Properties of Analytic Functions with Bounded Radius Rotations
International Mathematical Forum, Vol., 7, no. 4, 59-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.988/imf.7.665 Convolution and Subordination Properties of Analytic Functions with Bounded Radius Rotations
More informationTHE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS. Communicated by Mohammad Sal Moslehian. 1.
Bulletin of the Iranian Mathematical Society Vol. 35 No. (009 ), pp 119-14. THE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS R.M. ALI, S.K. LEE, V. RAVICHANDRAN AND S. SUPRAMANIAM
More informationA NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR. F. Ghanim and M. Darus. 1. Introduction
MATEMATIQKI VESNIK 66, 1 14, 9 18 March 14 originalni nauqni rad research paper A NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR F. Ghanim and M. Darus Abstract. In the present
More informationBOUNDEDNESS, UNIVALENCE AND QUASICONFORMAL EXTENSION OF ROBERTSON FUNCTIONS. Ikkei Hotta and Li-Mei Wang
Indian J. Pure Appl. Math., 42(4): 239-248, August 2011 c Indian National Science Academy BOUNDEDNESS, UNIVALENCE AND QUASICONFORMAL EXTENSION OF ROBERTSON FUNCTIONS Ikkei Hotta and Li-Mei Wang Department
More informationOn certain subclasses of analytic functions
Stud. Univ. Babeş-Bolyai Math. 58(013), No. 1, 9 14 On certain subclasses of analytic functions Imran Faisal, Zahid Shareef and Maslina Darus Abstract. In the present paper, we introduce and study certain
More informationA NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS. Abstract
A NOTE ON UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS M. Darus, R.W. Ibrahim Abstract The main object of this article is to introduce sufficient conditions of univalency for a class of analytic
More informationSubclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions
P a g e 52 Vol.10 Issue 5(Ver 1.0)September 2010 Subclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions G.Murugusundaramoorthy 1, T.Rosy 2 And K.Muthunagai
More informationBIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) Coefficients of the Inverse of Strongly Starlike Functions. ROSlHAN M.
BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY BIII/. Malaysinn Math. Sc. Soc. (Second Series) 26 (2003) 63-71 Coefficients of the Inverse of Strongly Starlike Functions ROSlHAN M. ALI School
More informationA SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3(2011, Pages 1-8. A SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS (COMMUNICATED
More informationRosihan M. Ali and V. Ravichandran 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol. 14, No. 4, pp. 1479-1490, August 2010 This paper is available online at http://www.tjm.nsysu.edu.tw/ CLASSES OF MEROMORPHIC α-convex FUNCTIONS Rosihan M. Ali and V.
More informationSufficient conditions for certain subclasses of meromorphic p-valent functions
Bol. Soc. Paran. Mat. (3s.) v. 33 (015): 9 16. c SPM ISSN-175-1188 on line ISSN-0037871 in ress SPM: www.sm.uem.br/bsm doi:10.569/bsm.v33i.1919 Sufficient conditions for certain subclasses of meromorhic
More informationCoefficient bounds for some subclasses of p-valently starlike functions
doi: 0.2478/v0062-02-0032-y ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN POLONIA VOL. LXVII, NO. 2, 203 SECTIO A 65 78 C. SELVARAJ, O. S. BABU G. MURUGUSUNDARAMOORTHY Coefficient bounds for some
More informationOn a subclass of n-close to convex functions associated with some hyperbola
General Mathematics Vol. 13, No. 3 (2005), 23 30 On a subclass of n-close to convex functions associated with some hyperbola Mugur Acu Dedicated to Professor Dumitru Acu on his 60th anniversary Abstract
More informationTwo Points-Distortion Theorems for Multivalued Starlike Functions
Int. Journal of Math. Analysis, Vol. 2, 2008, no. 17, 799-806 Two Points-Distortion Theorems for Multivalued Starlike Functions Yaşar Polato glu Department of Mathematics and Computer Science TC İstanbul
More informationInclusion relationships for certain classes of analytic functions involving the Choi-Saigo-Srivastava operator
Cho Yoon Journal of Inequalities Applications 2013, 2013:83 R E S E A R C H Open Access Inclusion relationships for certain classes of analytic functions involving the Choi-Saigo-Srivastava operator Nak
More informationOn a subclass of analytic functions involving harmonic means
DOI: 10.1515/auom-2015-0018 An. Şt. Univ. Ovidius Constanţa Vol. 231),2015, 267 275 On a subclass of analytic functions involving harmonic means Andreea-Elena Tudor Dorina Răducanu Abstract In the present
More informationA note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator
General Mathematics Vol. 17, No. 4 (2009), 75 81 A note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator Alina Alb Lupaş, Adriana Cătaş Abstract By means of
More informationSOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR. Let A denote the class of functions of the form: f(z) = z + a k z k (1.1)
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume LV, Number 1, March 2010 SOME APPLICATIONS OF SALAGEAN INTEGRAL OPERATOR Abstract. In this paper we introduce and study some new subclasses of starlike, convex,
More informationDIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ)
DIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ) Received: 05 July, 2008 RABHA W. IBRAHIM AND MASLINA DARUS School of Mathematical Sciences Faculty of Science and Technology Universiti
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 informationMajorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric Function
Tamsui Oxford Journal of Information and Mathematical Sciences 284) 2012) 395-405 Aletheia University Majorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric
More informationOn Multivalent Functions Associated with Fixed Second Coefficient and the Principle of Subordination
International Journal of Mathematical Analysis Vol. 9, 015, no. 18, 883-895 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.015.538 On Multivalent Functions Associated with Fixed Second Coefficient
More informationSubclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers
Acta Univ. Sapientiae, Mathematica, 10, 1018 70-84 DOI: 10.478/ausm-018-0006 Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers H. Özlem Güney Dicle University,
More informationRosihan M. Ali, M. Hussain Khan, V. Ravichandran, and K. G. Subramanian. Let A(p, m) be the class of all p-valent analytic functions f(z) = z p +
Bull Korean Math Soc 43 2006, No 1, pp 179 188 A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION Rosihan M Ali, M Hussain Khan, V Ravichandran, and K G Subramanian Abstract
More informationOn a class of analytic functions related to Hadamard products
General Mathematics Vol. 15, Nr. 2 3(2007), 118-131 On a class of analytic functions related to Hadamard products Maslina Darus Abstract In this paper, we introduce a new class of analytic functions which
More informationCoefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function
Malaya J. Mat. 43)206) 505 52 Coefficient Estimates for Bazilevič Ma-Minda Functions in the Space of Sigmoid Function Sunday Oluwafemi Olatunji a, and Emmanuel Jesuyon Dansu b a,b Department of Mathematical
More informationON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES
ON CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS AND RADIUS PROPERTIES M. OBRADOVIĆ and S. PONNUSAMY Let S denote the class of normalied univalent functions f in the unit disk. One of the problems addressed
More informationOn close-to-convex functions satisfying a differential inequality
Stud. Univ. Babeş-Bolyai Math. 60(2015), No. 4, 561 565 On close-to-convex functions satisfying a differential inequality Sukhwinder Singh Billing Abstract. Let C α(β) denote the class of normalized functions
More informationHankel determinant for p-valently starlike and convex functions of order α
General Mathematics Vol. 17, No. 4 009, 9 44 Hankel determinant for p-valently starlike and convex functions of order α Toshio Hayami, Shigeyoshi Owa Abstract For p-valently starlike and convex functions
More informationDIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS. Maslina Darus and Imran Faisal. 1. Introduction and preliminaries
FACTA UNIVERSITATIS (NIŠ) SER. MATH. INFORM. 26 (2011), 1 7 DIFFERENTIAL SUBORDINATION FOR MEROMORPHIC MULTIVALENT QUASI-CONVEX FUNCTIONS Maslina Darus and Imran Faisal Abstract. An attempt has been made
More informationSUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL DERIVATIVE OPERATOR
Sutra: International Journal of Mathematical Science Education Technomathematics Research Foundation Vol. 4 No. 1, pp. 17-32, 2011 SUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. (008), no., 16 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) http://www.math-analysis.org GENEALIZATION OF SǍLǍGEAN OPEATO FO CETAIN ANALYTIC FUNCTIONS ALAWIAH
More informationSubclasses of Analytic Functions. Involving the Hurwitz-Lerch Zeta Function
International Mathematical Forum, Vol. 6, 211, no. 52, 2573-2586 Suclasses of Analytic Functions Involving the Hurwitz-Lerch Zeta Function Shigeyoshi Owa Department of Mathematics Kinki University Higashi-Osaka,
More informationSTRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR. Anessa Oshah and Maslina Darus
Korean J. Math. 23 2015, No. 4, pp. 503 519 http://dx.doi.org/10.11568/jm.2015.23.4.503 STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah and Maslina
More informationSOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II
italian journal of pure and applied mathematics n. 37 2017 117 126 117 SOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II M. Kasthuri K. Vijaya 1 K. Uma School
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics INTEGRAL MEANS INEQUALITIES FOR FRACTIONAL DERIVATIVES OF SOME GENERAL SUBCLASSES OF ANALYTIC FUNCTIONS TADAYUKI SEKINE, KAZUYUKI TSURUMI, SHIGEYOSHI
More informationResearch Article A New Class of Meromorphic Functions Associated with Spirallike Functions
Applied Mathematics Volume 202, Article ID 49497, 2 pages doi:0.55/202/49497 Research Article A New Class of Meromorphic Functions Associated with Spirallike Functions Lei Shi, Zhi-Gang Wang, and Jing-Ping
More informationConvex Functions and Functions with Bounded Turning
Tamsui Oxford Journal of Mathematical Sciences 26(2) (2010) 161-172 Aletheia University Convex Functions Functions with Bounded Turning Nikola Tuneski Faculty of Mechanical Engineering, Karpoš II bb, 1000
More informationHarmonic Mappings for which Second Dilatation is Janowski Functions
Mathematica Aeterna, Vol. 3, 2013, no. 8, 617-624 Harmonic Mappings for which Second Dilatation is Janowski Functions Emel Yavuz Duman İstanbul Kültür University Department of Mathematics and Computer
More informationSOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR. Nagat. M. Mustafa and Maslina Darus
FACTA UNIVERSITATIS NIŠ) Ser. Math. Inform. Vol. 27 No 3 2012), 309 320 SOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR Nagat. M. Mustafa and Maslina
More informationStarlike Functions of Complex Order
Applied Mathematical Sciences, Vol. 3, 2009, no. 12, 557-564 Starlike Functions of Complex Order Aini Janteng School of Science and Technology Universiti Malaysia Sabah, Locked Bag No. 2073 88999 Kota
More informationResearch Article On Generalized Bazilevic Functions Related with Conic Regions
Applied Mathematics Volume 1, Article ID 9831, 1 pages doi:1.1155/1/9831 Research Article On Generalized Bazilevic Functions Related with Conic Regions Khalida Inayat Noor and Kamran Yousaf Department
More informationA New Subclasses of Meromorphic p-valent Functions with Positive Coefficient Defined by Fractional Calculus Operators
Volume 119 No. 15 2018, 2447-2461 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ http://www.acadpubl.eu/hub/ A New Subclasses of Meromorphic p-valent Functions with Positive Coefficient
More informationSubclasses of starlike functions associated with some hyperbola 1
General Mathematics Vol. 14, No. 2 2006, 31 42 Subclasses of starlike functions associated with some hyperbola 1 Mugur Acu Abstract In this paper we define some subclasses of starlike functions associated
More informationON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS
U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 1, 018 ISSN 13-707 ON CERTAIN CLASS OF UNIVALENT FUNCTIONS WITH CONIC DOMAINS INVOLVING SOKÓ L - NUNOKAWA CLASS S. Sivasubramanian 1, M. Govindaraj, K. Piejko
More informationConvolution Properties of Convex Harmonic Functions
Int. J. Open Problems Complex Analysis, Vol. 4, No. 3, November 01 ISSN 074-87; Copyright c ICSRS Publication, 01 www.i-csrs.org Convolution Properties of Convex Harmonic Functions Raj Kumar, Sushma Gupta
More informationAn Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
International Journal of Applied Engineering Research ISS 0973-4562 Volume 3 umber 6 (208 pp. 2494-2500 An Application of Wilf's Subordinating Factor Sequence on Certain Subclasses of Analytic Functions
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics APPLICATIONS OF DIFFERENTIAL SUBORDINATION TO CERTAIN SUBCLASSES OF MEROMORPHICALLY MULTIVALENT FUNCTIONS H.M. SRIVASTAVA AND J. PATEL Department
More informationHARMONIC CLOSE-TO-CONVEX MAPPINGS
Applied Mathematics Stochastic Analysis, 15:1 (2002, 23-28. HARMONIC CLOSE-TO-CONVEX MAPPINGS JAY M. JAHANGIRI 1 Kent State University Department of Mathematics Burton, OH 44021-9500 USA E-mail: jay@geauga.kent.edu
More informationle2 { Re d(a, f)l de > (1.2) n=2ar, 01 < e 2 ON ALPHA-CLOSE-TO-CONVEX FUNCTIONS OF ORDER BETA functions. f(z) z + z a n Re (1 ) zf + (I + zf"(z)) do >
Internat. J. Math. & Math. Sci. Vol. 9 No. 3 (1986) 435-438 435 ON ALPHA-CLOSE-TO-CONVEX FUNCTIONS OF ORDER BETA M.A. NASR Faculty of Science University of Mansoura Mansoura, Egypt (Received January 9,
More informationSUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA LINEAR OPERATOR
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 2, Issue 3(21), Pages 15-26. SUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA
More informationThe Relationships Between p valent Functions and Univalent Functions
DOI:.55/auom-25-5 An. Şt. Univ. Ovidius Constanţa Vol. 23(),25, 65 72 The Relationships Between p valent Functions and Univalent Functions Murat ÇAĞLAR Abstract In this paper, we obtain some sufficient
More informationResearch Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions
Abstract and Applied Analysis Volume 20, Article ID 59405, 0 pages doi:0.55/20/59405 Research Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric
More informationNotes on Starlike log-harmonic Functions. of Order α
Int. Journal of Math. Analysis, Vol. 7, 203, no., 9-29 Notes on Starlike log-harmonic Functions of Order α Melike Aydoğan Department of Mathematics Işık University, Meşrutiyet Koyu Şile İstanbul, Turkey
More informationSome Geometric Properties of a Certain Subclass of Univalent Functions Defined by Differential Subordination Property
Gen. Math. Notes Vol. 20 No. 2 February 2014 pp. 79-94 SSN 2219-7184; Copyright CSRS Publication 2014 www.i-csrs.org Available free online at http://www.geman.in Some Geometric Properties of a Certain
More informationDIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION
M athematical I nequalities & A pplications Volume 12, Number 1 2009), 123 139 DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION ROSIHAN M. ALI,
More informationResearch Article Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector
International Journal of Mathematics and Mathematical Sciences Volume 2011, Article ID 205845, 19 pages doi:10.1155/2011/205845 Research Article Differential Subordinations of Arithmetic and Geometric
More informationFekete-Szegö Inequality for Certain Classes of Analytic Functions Associated with Srivastava-Attiya Integral Operator
Applied Mathematical Sciences, Vol. 9, 015, no. 68, 3357-3369 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.543 Fekete-Szegö Inequality for Certain Classes of Analytic Functions Associated
More informationAbstract. For the Briot-Bouquet differential equations of the form given in [1] zu (z) u(z) = h(z),
J. Korean Math. Soc. 43 (2006), No. 2, pp. 311 322 STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS José A. Antonino Astract. For the Briot-Bouquet differential equations of
More informationCOEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS
Khayyam J. Math. 5 (2019), no. 1, 140 149 DOI: 10.2204/kjm.2019.8121 COEFFICIENTS OF BI-UNIVALENT FUNCTIONS INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH CHEBYSHEV POLYNOMIALS IBRAHIM T. AWOLERE 1, ABIODUN
More informationA Note on Coefficient Inequalities for (j, i)-symmetrical Functions with Conic Regions
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN (p) 2303-4874 ISSN (o) 2303-4955 wwwimviblorg /JOURNALS / BULLETIN Vol 6(2016) 77-87 Former BULLETIN OF THE SOCIETY OF MATHEMATICIANS BANJA
More informationOn a New Subclass of Meromorphically Multivalent Functions Defined by Linear Operator
International Mathematical Forum, Vol. 8, 213, no. 15, 713-726 HIKARI Ltd, www.m-hikari.com On a New Subclass of Meromorphically Multivalent Functions Defined by Linear Operator Ali Hussein Battor, Waggas
More informationNEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS
Kragujevac Journal of Mathematics Volume 42(1) (2018), Pages 83 95. NEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS M. ALBEHBAH 1 AND M. DARUS 2 Abstract. In this aer, we introduce a new
More informationCertain properties of a new subclass of close-to-convex functions
Arab J Math (212) 1:39 317 DOI 1.17/s465-12-29-y RESEARCH ARTICLE Pranay Goswami Serap Bulut Teodor Bulboacă Certain properties of a new subclass of close-to-convex functions Received: 18 November 211
More informationCtA, cc( ) ct,-l where S*() and C(-) denote the classes of starlike and convex 1-A
Internat. J. Math. & Math. Sci. VOL. 14 NO. 4 (1991) 741-746 741 ON RADII OF CONVEXITY AND STARLIKENESS OF SOME CLASSES OF ANALYTIC FUNCTIONS KHALIDA INAYAT NOOR Mathematics Department College of Science
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 informationON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS
LE MATEMATICHE Vol. LXIX 2014) Fasc. I, pp. 259 274 doi: 10.4418/2014.69.1.20 ON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS ALI MUHAMMAD - MARJAN SAEED In this
More informationResearch Article Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative
Hindawi Function Spaces Volume 217 Article ID 5739196 6 pages https://doi.org/1.1155/217/5739196 Research Article Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative Xiaofei
More informationDifferential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator
KYUNGPOOK Math. J. 512011, 217-232 DOI 10.5666/KMJ.2011.51.2.217 Differential Sandwich Theorem for Multivalent Meromorhic Functions associated with the Liu-Srivastava Oerator Rosihan M. Ali, R. Chandrashekar
More informationSome basic properties of certain subclasses of meromorphically starlike functions
Wang et al. Journal of Inequalities Applications 2014, 2014:29 R E S E A R C H Open Access Some basic properties of certain subclasses of meromorphically starlike functions Zhi-Gang Wang 1*, HM Srivastava
More informationOn certain subclasses of analytic functions associated with generalized struve functions
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 3(79), 2015, Pages 3 13 ISSN 1024 7696 On certain subclasses of analytic functions associated with generalized struve functions G.
More informationSubclass of Meromorphic Functions with Positive Coefficients Defined by Frasin and Darus Operator
Int. J. Open Problems Complex Analysis, Vol. 8, No. 1, March 2016 ISSN 2074-2827; Copyright c ICSRS Publication, 2016 www.i-csrs.org Subclass of Meromorphic Functions with Positive Coefficients Defined
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 informationON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS
Nunokawa, M. and Sokół, J. Osaka J. Math. 5 (4), 695 77 ON SOME LENGTH PROBLEMS FOR ANALYTIC FUNCTIONS MAMORU NUNOKAWA and JANUSZ SOKÓŁ (Received December 6, ) Let A be the class of functions Abstract
More informationA. Then p P( ) if and only if there exists w Ω such that p(z)= (z U). (1.4)
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More informationCoefficients estimates of some subclasses of analytic functions related with conic domain
DOI: 10.2478/auom-2013-0031 An. Şt. Univ. Ovidius Constanţa Vol. 212),2013, 181 188 Coefficients estimates of some subclasses of analytic functions related with conic domain Abstract In this paper, the
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 informationResearch Article Some Inclusion Relationships of Certain Subclasses of p-valent Functions Associated with a Family of Integral Operators
ISRN Mathematical Analysis Volume 2013, Article ID 384170, 8 pages http://dx.doi.org/10.1155/2013/384170 Research Article Some Inclusion Relationships of Certain Subclasses of p-valent Functions Associated
More informationCOEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS
Bull. Korean Math. Soc. 0 (0), No. 0, pp. 1 0 https://doi.org/10.4134/bkms.b170051 pissn: 1015-8634 / eissn: 2234-3016 COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS Ebrahim Analouei
More informationResearch Article Coefficient Conditions for Harmonic Close-to-Convex Functions
Abstract and Applied Analysis Volume 212, Article ID 413965, 12 pages doi:1.1155/212/413965 Research Article Coefficient Conditions for Harmonic Close-to-Convex Functions Toshio Hayami Department of Mathematics,
More informationFekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination
Mathematica Aeterna, Vol. 3, 203, no. 3, 93-99 Fekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination B. Srutha Keerthi Department of Applied Mathematics Sri
More informationReuiata Colombiana de Matem~ti~a6 v o t., XII (1978l~ pttgf..o 83-96
Reuiata Colombiana de Matem~ti~a6 v o t. XII (1978l~ pttgf..o 83-96 SPECIAL ARITHMETIC AND GEOMETRIC MEANS PRESERVE ~-LIKE UNIVALENCE by S K. BAJPAI Let R be a region containing O.Let ~ be analytic in
More informationSubordinate Solutions of a Differential Equation
Subordinate Solutions of a Differential Equation Stacey Muir Abstract In 2003, Ruscheweyh and Suffridge settled a conjecture of Pólya and Schoenberg on subordination of the de la Vallée Poussin means of
More information