COMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE
|
|
- Caroline McKinney
- 6 years ago
- Views:
Transcription
1 COMMON FIXED POINT THEOREM OF THREE MAPPINGS IN COMPLETE METRIC SPACE Latpate V.V. and Dolhare U.P. ACS College Gangakhed DSM College Jintur Abstract:-In this paper we prove common fixed point theorem of weakly compatible mappings in complete Metric space. AMS Subject classification:-47h0,47h09 Keywords:-Fixed point, Common fixed point, contraction mapping, weakly compatible mapping. I. INTRODUCTION The study of common fixed point of mappings satisfying contractive type conditions has been a very active field of research activity during the last some decades. The fixed point theory has several applications in many fields of science and engineering field.s. Banach [ ] derived a well known theorem for a contraction mapping in a complete Metric space, which states that, A contraction has a unique fixed point theorem in a complete Metric space. After that many authors proved fixed point theorems for mappings satisfying certain contraction conditions. In 968 R. Kanan [ 5 ] introduced another type of map called as Kanan map and investigated unique fixed point theorem in complete Metric space. In 973 B.K. Das and Sattya Gupta [ ] Generalized Banach Contraction Principle in terms of rational expression.various fixed point thereoms proved by several authors. Recently V.V. Latpate and Dolhare U.P.[ 6 ] proved fixed point theorems for uniformly locally contractive mappings. Sesa [ 8 ] Introduced a concept of weakly commuting mappings and obtained some common fixed point theorems in complete Metric space. S.T. Patil [ 7 ] Proved some common fixed point theorems for weakly commuting mappings satisfying a contractive conditions in complete Metric space. In 986 G. Jungck [ 4 ] defined compatible mappings and proved some common fixed point theorems in complete Metric space. Also he proved weak commuting mappings are compatible. Also we prove the common fixed point theorem of weakly compatible mappings satisfying the inequality similar to C- Contraction. II. PRELIMINARIES Definition.:- Let X be a non-empty set. A mapping d : X X R is said to be a Metric or a distance function if it satisfies following conditions.. d( x, y is non-negative.. d( x, y =0 if and only if x and y coincides i.e. x = y. 3. d( x, y d( y, x (Symmetry 4. d( x, y d( x, z d( z, y (Triangle inequality Then the function d is referred to as metric on X. And (X,d or simply X is said to as Metric space. Definition.:- A Metric space (X,d is said to be a complete Metric space if every Cauchy sequence in X converges to a point of X. Definition.3:- If (X,d be a complete Metric space and a function F : X X is said to be a contraction map if d( F( x, F( y d( x, y DOI:0.63/IJAPSA QZLGT Page
2 Volume 03, Issue 8, [August- 07] e-issn: , p-issn: X For all x, yòx and for 0 Definition.4:- Let F : X X, then x ò X is said to be a fixed point of F if F( x x Definition.5:-Let X be a Metric space and if F and F be any two maps. An element a ò X is said to be a common fixed point of F and F if F( a F( a For ex:- If F( x sin( x and F( x tan( x Then 0 is the common fixed point F and F Since F (0 sin(0 and F (0 tan(0 0 Definition.6:-( S.K. Chatterjea [ 3 ] A mapping F : X X where (X,d is a Metric space is said to be C-Contraction if there is a some s.t. 0 s.t. the following inequality holds d F, F ( d( x, F d( y, F ( x y y x If ( Xd, be a complete Metric space, then any C-contraction on X has a unique fixed point. Definition.7:- Let F and G be two self mappings of a Metric space ( Xd,. F and G are said to be weakly compatible if for all xx ò Fx Gx FGx GFx Theorem.:-Suppose P,Q,R,S be four self maps of a Metric space (X,d which satisfies the conditions given below.. P( X S( X and R( X Q( X.. Pair of mappings (P,Q and (R,S are Commuting. 3. One of the function P, Q, R, S is continuous. 4. d( Px, Rx ( x, y where ( x, y max d( Qx, Sy, d( Qx, Px, d( Sy, Ry For all x, y ò X and 0 and 5. X is complete. Then P,Q,R and S have Unique Common Fixed point zx ò.further more z is the unique common fixed point of (P,Q and (R,S. Theorem.:- Let (X,d be a Complete Metric space. Suppose that the mappings P,Q,R and S are four self maps of X which satisfies the following, S(X P( x and R( X Q( X ; d(rx,sx ( ( xy, Where is an upper semi continuous, contractive modulus and ( x, y max { d( Px, Qy, d( Px, Rx, d( Qy, Sy, ( d( Px, Sy d( Qy, Rx} 3. The pairs (R,P and (S,Q are weakly compatible. Then P,Q,R and S have a unique common fixed point. We obtain Common Fixed point theorems for three maps which satisfies contraction condition. III. MAIN RESULT Theorem 3.:- Let ( Xd, be a complete Metric space and Let A be a non empty closed subset of X. Let P, Q : A A be s.t. d( P, Q ( d( R, Q d( R, P d( S, R ( d( R, Q d( R, P (. x y x y y x x y x y y All rights Reserved Page
3 Volume 03, Issue 8, [August- 07] e-issn: , p-issn: X For any ( x, y ò X X, where a function :[0, [0, is a continuous and ( xy, 0 iff x y 0 and R : A X which satisfies the following condition. (i PA RA and QA RA (ii The pair of mappings (P,R and (Q,R are weakly compatible. (iii R(A is closed subset of X. Then P,R and Q have unique common fixed point. Proof:- Let x 0 be any arbitrary element of A as PA RA and QA RA. y0 Px0 Rx, y Qx Rx, y Px Rx3,... Let { x n } and{ y n } be two sequences s.t.... y Px Rx, y Qx Rx,... First we shall prove that d( yn, yn 0 as n Let n=k by inequality (, we have d( y, y d( Px, Qx n k k k n n n n n n ( d ( Rx, Qx d( Rx, Px d ( Sx (,,,, k k k k k Rx k d ( Rx Qx d k k ( Rx Px k k ( d( y, y d( y, (, ( y d y y ( d y, y, d( y, y k k k k k k k k k k ( y y d ( k, k (. ( d( y k, y k d ( y k,y k This gives d( y, y d( y, y k k k k For n=k+, similarly, we can show that d( yk, yk d( y k, yk (.3 d( yn, yn is a non-increasing sequence of non-negative real numbers and hence it is convergent. Let l lim d( yn, yn From (. we have n d( yn, yn d( yn, yn and by triangle inequality d( yn, yn ( d( yn, yn d( yn, yn (.4 Letting n, we have lim d( yn, yn lim d( yn, yn lim d( yn, yn n n n l lim d ( yn, yn l n lim d( y, y =l n n All rights Reserved Page 3
4 Consider d( y, y d( Px, Qx k k k k Volume 03, Issue 8, [August- 07] e-issn: , p-issn: X ( d( y k, y k d( y k, y k d( y k, y k ( d( y k, y k, d( yk, y k (.5 Letting k and Since is given to be continuous we obtain l l ( l,0 This gives ( l,0 0 By definition of, ( x, y 0 if x y 0 l 0, l 0 l lim d( yn, yn 0 (.5 n Now our claim is that { y n } is a Cauchy sequence From (.3 we have d( y, y d( y, y, n n n n To prove { y n } is a Cauchy sequence we only prove that the subsequence { y n } is a Cauchy. If possible suppose that { y n } is not a Cauchy sequence. There exists 0 for which we can find two subsequence s { y nk ( } and { y mk ( } of { y n } Such that n k is the least index for which n k > m k >k and d( y mk (, y nk ( This gives Using triangle inequality d ( y, y m( k n( k d( y, y d( y, y m( k n( k m( k n( k n( k n( k n( k n( k (.6 d( y, y d( y, y (.7 Now as k and from (.6, we have lim k d( y m( k, y n( k (.8 d( y, y d( y, y d( y, y (.9 Also And m( k n( k m( k n( k n( k n( k d( y, y d( y, y d( y, y (.0 n( k m( k n( k m( k m( k m( k d( y, y d( y, y d( y, y (. n( k m( k n( k m( k m( k m( k From (.6,(.9,(.0 and (., We have lim d( y, y lim d( y, y k m( k n( k k m( k n( k Inequality (. gives d(, y d( Px, Qx y m( k n( k n( k m( k = lim d( y, y ò k m( k n( k All rights Reserved Page 4
5 Volume 03, Issue 8, [August- 07] e-issn: , p-issn: X ( d ( Rx (, Qx ( d ( Rx (, Px ( d ( Sx (, Rx n k m k m k n k n k m( k ( d( Rx, Qx, d( Rx, Px n( k m( k m( k n( k d( y n( k, y m( k d( y m( k, y n( k d( y n( k, y m( k ( d( y, y, d( y, y n( k m( k m( k n( k ( d( y, ( m( k y m( k d y m( k, y m( k (.3 Letting k in above inequality and from (.3 and is continuous, We have ( ( this gives (, 0. By assumption of ( x, y 0 if x y 0 0. But 0 therefore which is contradiction. { y n } is a Cauchy Sequence. To prove P,Q,R have a Common fixed point. Given (X,d be complete and { Sequence, there is px ò y p y } s.t. lim n as A is closed and { n n closed.so there is ua ò s.t. p= Ru for every nn ò d( Pu, y d( Pu, Qx n n n n y n } be Cauchy A, pa ò, By hypothesis R(A is ( d ( Ru, Qx d ( Rx, Pu d ( Su, Rx n n n (.4 - ( d( Ru, Qx, d( Rx, Pu When n ( d ( p, y d ( y, Pu d ( Su n n, y n ( d( Ru, Qx, d( Rx, Pu n n d( Pu, p ( d ( p, p d ( p, Pu d ( Su, p ( d ( Ru, p, d ( p, Pu And hence (0, d( p, Pu ( d( Pu, p d( Su, p 0, d( p, pu 0Pu p Simillarly we can show that Su p. Pu Qu Ru p. Given pairs (R,P and (R,Q are weakly compatible, Pp Qp Rp Now consider d( Pp, y d( Pp, Qx n n ( d ( Rp, Qx d ( Rx, Pp d ( Sp, Rx n n n (.5 - ( d( Rp, Qx, d( Rx, Pp n All rights Reserved Page 5
6 Volume 03, Issue 8, [August- 07] e-issn: , p-issn: X ( d ( Rp, y d ( y, Pp d ( Sp, y n n n ( d( Rp, y, d( y, Pp n n As n, Since Pp Qp Rp, We have d ( Pp, p ( d ( Pp, p d ( p, Pp d ( Sp, p ( d ( Pp, p, d (, P p p (.6 Hence ( d( Pp, p, d( p, Pp 0 and so d( Pp, p 0 Pp p and from Pp Qp Rp We have Pp Qp Rp p. Thus Uniqueness of common fixed point is easily obtained from inequality (. IV. CONCLUSION Thus we proved common fixed point theorem for weakly compatible mappings. We are thankful to all authors. V. ACKNOWLEDGEMENT BIBLIOGRAPHY [] S.Banach,Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 3,(9 338 (French [] B.K. Das and S. Gupta, An extension of Banach Contraction principle through Rational expression. [3] S.K.Chattterjea, Fixed point theorems, C.R. Acad.Buglare Sci.,5 (97 [4] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Sci. 9, [5] (986, [6] Kanan R. (968 Some results on fixed points Bull. Calcutta Math. Soc., 60,7-76. [7] Latpate V.V. and Dolhare U.P., Uniformly Locally contractive mapping and fixed point theorems in generalized Metric space.ijapsa,06, [8] S.T. Patil, Results on fixed points and its applications,ph.d. thesis, Marathwada University, Aurangabad, India 990. [9] Sesa,S., on weakly commutativity condition in a fixed point consideration, Publ. Int. Math. 3(46 All rights Reserved Page 6
A Common Fixed Point Theorem in M-Fuzzy Metric Spaces for Integral type Inequality
International Journal of Theoretical & Applied Sciences Special Issue-NCRTAST 81: 113-1192016 ISSN No Print: 0975-1718 ISSN No Online: 2249-3247 A Common Fixed Point Theorem in M-Fuzzy Metric Spaces for
More informationFIXED POINT RESULTS IN SELF MAPPING FUNCTIONS
Int. J. Engg. Res. & Sci. & Tech. 2016 M Ramana Reddy, 2016 Research Paper ISSN 2319-5991 www.ijerst.com Vol. 5, No. 4, November 2016 2016 IJERST. All Rights Reserved FIXED POINT RESULTS IN SELF MAPPING
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 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 informationFixed Point Theorems via Absorbing Maps
Thai Journal of Mathematics Volume 6 (2008) Number 1 : 49 60 www.math.science.cmu.ac.th/thaijournal Fixed Point Theorems via Absorbing Maps U. Mishra, A. S. Ranadive and D. Gopal Abstract : The purpose
More informationQuadruple Coincidence Point Results in Partially Ordered Metric Spaces
BULLETIN OF THE INTERNATIONAL MATHEMATICAL VIRTUAL INSTITUTE ISSN p 2303-367 ISSN o 2303-955 wwwimviblorg / JOURNALS / BULLETIN OF IMVI Vol 201 5-52 doi: 117251/BIMVI10105G Former BULLETIN OF SOCIETY OF
More informationJournal of Shivaji University (Science & Technology) SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION.
SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION. Deepti Thakur and Sushil Sharma Department of Mathematics, Madhav Vigyan Mahavidhyalaya, Vikram University, Ujjain
More informationBest proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces
An. Şt. Univ. Ovidius Constanţa Vol. 20(3), 2012, 51 64 Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces Erdal Karapınar Abstract In this manuscript, the existence
More informationCOMMON FIXED POINT WITH CONTRACTIVE MODULUS ON REGULAR CONE METRIC SPACE VIA CONE C-CLASS FUNCTION
International J. of Math. Sci. & Engg. Appls. (IJMSEA) ISSN 0973-944, Vol. No. II (August, 07), pp. 43-6 COMMON FIXED POINT WITH CONTRACTIVE MODULUS ON REGULAR CONE METRIC SPACE VIA CONE C-CLASS FUNCTION
More informationInternational Journal of Mathematical Archive-5(10), 2014, Available online through ISSN
International Journal of Mathematical Archive-5(10), 2014, 217-224 Available online through www.ijma.info ISSN 2229 5046 COMMON FIXED POINT OF WEAKLY COMPATIBLE MAPS ON INTUITIONISTIC FUZZY METRIC SPACES
More informationSome Results of Compatible Mapping in Metric Spaces
International Refereed Journal of Engineering and Science (IRJES) ISSN (Online) 2319-183X, (Print) 2319-1821 Volume 6, Issue 3 (March 2017), PP.38-44 Some Results of Compatible Mapping in Metric Spaces
More informationCommon Fixed Point Theorem in Complex Valued Metric Spaces
ISSN: 219-875 (An ISO 297: 2007 Certified Organization) Vol. 2, Issue 12, December 201 Common Fixed Point Theorem in Complex Valued Metric Spaces Dr. Yogita R. Sharma Head, Department of Mathematics, Saffrony
More informationCommon Fixed Point Theorems for Two Pairs of Weakly Compatible Mappings in Fuzzy Metric Spaces Using (CLR ST ) Property
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 12, Issue 6 Ver. I (Nov. - Dec.2016), PP 66-71 www.iosrjournals.org Common Fixed Point Theorems for Two Pairs of Weakly
More informationarxiv: v1 [math.fa] 9 Mar 2009
Two Fixed-Point Theorems For Special Mappings A. Beiranvand, S. Moradi, M. Omid and H. Pazandeh arxiv:0903.504v [math.fa] 9 Mar 009 Faculty of Science, Department of Mathematics Arak University, Arak,
More informationCOMMON FIXED POINT THEOREMS IN CONE RECTANGULAR METRIC SPACES
International J. of Pure & Engg. Mathematics (IJPEM) ISSN 2348-3881, Vol. 3 No. II (August, 2015), pp. 125-135 COMMON FIXED POINT THEOREMS IN CONE RECTANGULAR METRIC SPACES SUNANDA R. PATIL 1 AND J. N.
More informationCommon Fixed Point Results in S-metric Spaces
Journal of Advances in Applied Mathematics, Vol. 4, No. 2, April 2019 https://dx.doi.org/10.22606/jaam.2019.42002 45 Common Fixed Point Results in S-metric Spaces Jierong Yao * and Liping Yang School of
More informationCommon Random Fixed Point theorem for compatible random multivalued operators
IOSR Journal of Mathematics (IOSR-JM) ISSN: 78-578. Volume, Issue (Sep-Oct. 0), PP9-4 Common Random Fixed Point theorem for compatible random multivalued operators Dr. Neetu Vishwakarma Abstract: The aim
More informationCOMMON FIXED POINT THEOREMS OF WEAK RECIPROCAL CONTINUITY IN METRIC SPACES. Saurabh Manro 1, Sanjay Kumar 2, Satwinder Singh Bhatia 3, Shin Min Kang 4
International Journal of Pure and Applied Mathematics Volume 88 No. 2 2013, 297-304 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v88i2.11
More informationAvailable online at Adv. Fixed Point Theory, 3 (2013), No. 4, ISSN:
Available online at http://scik.org Adv. Fixed Point Theory, 3 (2013), No. 4, 595-599 ISSN: 1927-6303 A COMMON FIXED POINT THEOREM UNDER ϕ-contractive CONDITIONS PH.R. SINGH 1,, AND M.R. SINGH 2, 1 Department
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 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 Theorem in Fuzzy Metric Space Using (CLRg) Property
International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 5 Issue 4 April 2016 PP.35-39 Fixed Point Theorem in Fuzzy Metric Space Using (CLRg) Property
More informationCommon Fixed Point of Four Mapping with Contractive Modulus on Cone Banach Space via cone C-class function
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume 3, Number 9 (207), pp. 5593 560 Research India Publications http://www.ripublication.com/gjpam.htm Common Fixed Point of Four Mapping
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 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 informationA GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 1(2017), Pages 92-108. A GENERALIZATION OF CONTRACTION PRINCIPLE IN QUASI-METRIC SPACES HAMZA
More informationFixed point theorems of nondecreasing order-ćirić-lipschitz mappings in normed vector spaces without normalities of cones
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 18 26 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa Fixed point theorems of nondecreasing
More informationBhavana Deshpande COMMON FIXED POINT RESULTS FOR SIX MAPS ON CONE METRIC SPACES WITH SOME WEAKER CONDITIONS. 1. Introduction and preliminaries
F A S C I C U L I M A T H E M A T I C I Nr 43 2010 Bhavana Deshpande COMMON FIXED POINT RESULTS FOR SIX MAPS ON CONE METRIC SPACES WITH SOME WEAKER CONDITIONS Abstract. The existence of coincidence points
More informationCommon Fixed Point Theorem Governed by Implicit Relation and Property (E. A.)
Common Fixed Point Theorem Governed by Implicit Relation and Property (E. A.) G. P. S. Rathore 1, Bijendra Singh 2, Kirty Chauhan 3 College of Horticulture, Mandsaur, India 1 S.S. in Mathematics, Vikram
More informationOccasionally Weakly Compatible Mapping in Cone Metric Space
Applied Mathematical Sciences, Vol. 6, 2012, no. 55, 2711-2717 Occasionally Weakly Compatible Mapping in Cone Metric Space Arvind Bhatt Applied Science Department (Mathematics) Bipin trpathi Kumaun institute
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 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 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 informationCommon Fixed Point Results in Complex Valued Metric Spaces with (E.A) and (CLR) Properties
Advances in Analysis, Vol., No. 4, October 017 https://dx.doi.org/10.606/aan.017.400 47 Common Fixed Point Results in Complex Valued Metric Spaces with (E.A) (CLR) Properties Mian Bahadur Zada 1, Muhammad
More informationCommon fixed point of -approximative multivalued mapping in partially ordered metric space
Filomat 7:7 (013), 1173 118 DOI 1098/FIL1307173A Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://wwwpmfniacrs/filomat Common fixed point of -approximative
More informationCommon Fixed Point Theorems for T-Weak Contraction Mapping in a Cone Metric Space
Mathematica Aeterna, Vol. 3, 2013, no. 2, 121-131 Common Fixed Point Theorems for T-Weak Contraction Mapping in a Cone Metric Space A.K.Dubey Department of Mathematics, Bhilai Institute of Technology,
More informationNew extension of some fixed point results in complete metric spaces
DOI 10.1515/tmj-017-0037 New extension of some fixed point results in complete metric spaces Pradip Debnath 1,, Murchana Neog and Stojan Radenović 3 1, Department of Mathematics, North Eastern Regional
More informationCOMMON FIXED POINT THEOREMS FOR CYCLIC WEAK
Available online at http://scik.org Adv. Inequal. Appl. 204, 204:38 ISSN: 2050-746 COMMON FIXED POINT THEOREMS FOR CYCLIC WEAK, ψ-contractions IN MENGER SPACES S.M. ROOSEVELT,, K.S. DERSANAMBIKA 2 Department
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 informationMultiplicative metric spaces and contractions of rational type
Advances in the Theory of Nonlinear Analysis and its Applications 2 (2018) No. 4, 195 201. https://doi.org/10.31197/atnaa.481995 Available online at www.atnaa.org Research Article Multiplicative metric
More informationFixed Point Theorems for Generalized β φ contractive Pair of Mappings Using Simulation Functions
Bol. Soc. Paran. Mat. (3s.) v. 00 0 (0000):????. c SPM ISSN-175-1188 on line ISSN-0037871 in press SPM: www.spm.uem.br/bspm doi:10.569/bspm.40870 Fixed Point Theorems for Generalized β φ contractive Pair
More informationCommon Fixed Point Theorems of Generalized Contractive Mappings Using Weak Reciprocal Continuity
Int. Journal of Math. Analysis, Vol. 8, 204, no. 2, 07-026 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ijma.204.4369 Common Fixed Point Theorems of Generalized Contractive Mappings Using Weak
More informationHigher Portfolio Quadratics and Polynomials
Higher Portfolio Quadratics and Polynomials Higher 5. Quadratics and Polynomials Section A - Revision Section This section will help you revise previous learning which is required in this topic R1 I have
More informationA NOTE ON COMMON FIXED POINT THEOREMS IN PARTIAL METRIC SPACES
Miskolc Mathematical Notes HU e-issn 1787-2413 Vol. 12 (2011), No. 2, pp. 185 191 A NOTE ON COMMON FIXED POINT THEOREMS IN PARTIAL METRIC SPACES ERDAL KARAPINAR Received February 16, 2011 Abstract. In
More informationCOMMON FIXED POINT THEOREMS FOR SIX WEAKLY COMPATIBLE SELF-MAPPINGS IN M- FUZZY METRIC SPACES
COMMON FIXED POINT THEOREMS FOR SIX WEAKLY COMPATIBLE SELF-MAPPINGS IN M- FUZZY METRIC SPACES 1 N. Appa Rao, 2 Dr. V. Dharmaiah, 1 Department of Mathematics Dr. B.R. Ambedkar Open University Hyderabad
More informationCOMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES
STUDIA UNIV. BABEŞ BOLYAI MATHEMATICA Volume XLVII Number 1 March 00 COMMON FIXED POINT THEOREMS FOR MULTIVALUED OPERATORS ON COMPLETE METRIC SPACES 1. Introduction The purpose of this paper is to prove
More informationCOUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
Kragujevac Journal of Mathematics Volume 382 2014, Pages 249 257. COUPLED FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES STOJAN RADENOVIĆ Abstract. In this paper, by reducing
More informationFixed Point Theorems in 2- Metric Space with Continuous Convex Structure
Vol6, No2, 2016 wwwiisteorg Fixed Point Theorems in 2- Metric Space with Continuous Convex Structure Nidhi Gargav 1*, Geeta Modi 2, Rizwana Jama 1 Department of Mathematics, Saifia Science PG College Bhopal
More informationFixed point theorems in fuzzy metric spaces using (CLRG) property
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2015, 6(6):17-22 ISSN: 0976-8610 CODEN (USA): AASRFC Fixed point theorems in fuzzy metric spaces using (CLRG) property
More informationCommon Fixed Point Theorems For Weakly Compatible Mappings In Generalisation Of Symmetric Spaces.
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn:2319-765x. Volume 9, Issue 1 (Nov. Dec. 2013), PP 01-05 Common Fixed Point Theorems For Weakly Compatible Mappings In Generalisation Of Symmetric
More informationA Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity
Mathematica Moravica Vol. 10 (2006), 55 60 A Common Fixed Point Theorem for Multivalued Mappings Through T-weak Commutativity I. Kubiaczyk and Bhavana Deshpande Abstract. In this paper, we prove a common
More informationFixed Point Theorem in Cone B-Metric Spaces Using Contractive Mappings
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 7 (2017), pp. 2997-3004 Research India Publications http://www.ripublication.com Fixed Point Theorem in Cone B-Metric Spaces
More informationA Fixed Point Theorem Satisfying a Generalized. Weak Contractive Condition of Integral Type
Int. Journal of Math. Analysis, Vol. 6, 2012, no. 38, 1883 1889 A Fixed Point Theorem Satisfying a Generalized Weak Contractive Condition of Integral Type Vishal Gupta Department of Mathematics Maharishi
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 informationCommon Fixed Point Theorems for Compatible Mappings in Dislocated Metric Space
International Journal of Mathematical Analysis Vol. 9, 2015, no. 45, 2235-2242 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.57177 Common Fixed Point Theorems for Compatible Mappings
More informationMath 140A - Fall Final Exam
Math 140A - Fall 2014 - Final Exam Problem 1. Let {a n } n 1 be an increasing sequence of real numbers. (i) If {a n } has a bounded subsequence, show that {a n } is itself bounded. (ii) If {a n } has a
More informationCoincidence and Common Fixed Points in Symmetric Spaces under Implicit Relation and Application
International Mathematical Forum, 3, 2008, no. 30, 1489-1499 Coincidence and Common Fixed Points in Symmetric Spaces under Implicit Relation and Application H. K. Pathak School of Studies in Mathematics
More informationFIXED POINT POINTS OF RATIONAL TYPE CONTRACTIONS IN MULTIPLICATIVE METRIC SPACES. Dong-A University Busan 49315, KOREA 2 Department of Mathematics
International Journal of Pure Applied Mathematics Volume 106 No. 2 2016, 593-609 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v106i2.22
More informationFixed point theorems for generalized contraction mappings in multiplicative metric spaces
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 237 2363 Research Article Fixed point theorems for generalized contraction mappings in multiplicative metric spaces Afrah A. N. Abdou
More informationPAijpam.eu COMMON FIXED POINT THEOREMS OF COMPATIBLE MAPPINGS IN METRIC SPACES
International Journal of Pure and Applied Mathematics Volume 84 No. 203, 7-83 ISSN: 3-8080 (printed version); ISSN: 34-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v84i.3
More informationThe (CLR g )-property for coincidence point theorems and Fredholm integral equations in modular metric spaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 1, No., 17, 38-54 ISSN 137-5543 www.ejpam.com Published by New York Business Global The (CLR g )-property for coincidence point theorems and Fredholm
More information1 Introduction and preliminaries
Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 5: (0), 5 3 DOI: 0.98/FIL05D MULTIVALUED GENERALIZATIONS OF THE KANNAN FIXED POINT THEOREM
More informationA Common FIXED POINT THEOREM for weakly compatible mappings in 2-metric Spaces
American Journal of Mathematics and Sciences Vol. 5, No.1, (January-December, 2016) Copyright Mind Reader Publications ISSN No: 2250-3102 www.journalshub.com A Common FIXED POINT THEOREM for weakly compatible
More informationCommon fixed point theorems in Menger space with special reference to coincidence points
Available online at www.pelagiaresearchlibrary.com Advances in Applied Science Research, 2015, 6(7):224-229 ISSN: 0976-8610 CODEN (USA): AASRFC Common fixed point theorems in Menger space with special
More informationFuzzy fixed point of multivalued Ciric type fuzzy contraction mappings in b-metric spaces
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume, Number (06), pp. 307-36 Research India Publications http://www.ripublication.com Fuzzy fixed point of multivalued Ciric type fuzzy
More informationCommon Fixed Point Theorem for Six Maps in. d-complete Topological Spaces
Int. Journal of Math. Analysis, Vol. 6, 202, no. 4, 204-2047 Common Fixed Point Theorem for Six Maps in d-complete Topological Spaces Rahul Tiwari Department of Mathematical Sciences A.P.S. University,
More informationCommon fixed point results for multi-valued mappings with some examples
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 787 798 Research Article Common fixed point results for multi-valued mappings with some examples Afrah Ahmad Noan Abdou Department of
More informationMath 421, Homework #9 Solutions
Math 41, Homework #9 Solutions (1) (a) A set E R n is said to be path connected if for any pair of points x E and y E there exists a continuous function γ : [0, 1] R n satisfying γ(0) = x, γ(1) = y, and
More informationNON-SELF MAPPINGS UNDER COMMON LIMIT RANGE PROPERTY IN SYMMETRIC SPACES AND FIXED POINTS
TWMS J. App. Eng. Math. V.8, N.1, 018, pp. 0-31 NON-SELF MAPPINGS UNDER COMMON LIMIT RANGE PROPERTY IN SYMMETRIC SPACES AND FIXED POINTS SUMIT CHANDOK 1, DEEPAK KUMAR, Abstract. In this paper, some sufficient
More informationContraction Mapping in Cone b-hexagonal Metric Spaces
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 6 (2017), pp. 1651 1662 Research India Publications http://www.ripublication.com/gjpam.htm Contraction Mapping in Cone b-hexagonal
More informationFunctions. Chapter Continuous Functions
Chapter 3 Functions 3.1 Continuous Functions A function f is determined by the domain of f: dom(f) R, the set on which f is defined, and the rule specifying the value f(x) of f at each x dom(f). If f is
More informationGeneral Mathematics,Vol. 16, Nr. 1 (2008), On A Version of The Banach s Fixed Point Theorem 1
General Mathematics,Vol. 16, Nr. 1 (2008), 25 32 On A Version of The Banach s Fixed Point Theorem 1 C. O. Imoru, M. O. Olatinwo, G. Akinbo, A. O. Bosede Abstract Banach in 1922 proved the celebrated result
More informationA Common Fixed Point Theorems in Menger(PQM) Spaces with Using Property (E.A)
Int. J. Contemp. Math. Sciences, Vol. 6, 2011, no. 4, 161-167 A Common Fixed Point Theorems in Menger(PQM) Spaces with Using Property (E.A) Somayeh Ghayekhloo Member of young Researchers club, Islamic
More informationCOINCIDENCE AND COMMON FIXED POINT THEOREMS FOR FAINTLY COMPATIBLE MAPS
TWMS J. App. Eng. Math. V.7, N.1, 2017, pp. 25-32 COINCIDENCE AND COMMON FIXED POINT THEOREMS FOR FAINTLY COMPATIBLE MAPS ANITA TOMAR 1, SHIVANGI UPADHYAY 1, Abstract. The paper is aimed to generalize
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
More informationCommon Fixed Point Theorem Satisfying Implicit Relation On Menger Space.
www.ijecs.in International Journal Of Engineering And Computer Science ISSN:2319-7242 Volume 5 Issue 09 September 2016 Page No.18180-18185 Common Fixed Point Theorem Satisfying Implicit Relation On Menger
More informationFixed points and functional equation problems via cyclic admissible generalized contractive type mappings
Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 9 (2016), 1129 1142 Research Article Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011
Some common fixed point theorems for occasionally weakly compatible mappings in Fuzzy metric spaces Malhotra S.K 1, Navin Verma 2, Ravindra Sen 3 1- Department of Mathematics, Govt. S.G.S.P.G. College
More informationCOMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES
Available online at http://scik.org Adv. Fixed Point Theory, 7 (2017), No. 3, 451-457 ISSN: 1927-6303 COMMON RANDOM FIXED POINTS UNDER QUASI CONTRACTION CONDITIONS IN SYMMETRIC SPACES Maulana Azad National
More informationFIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY. 1. Introduction. Novi Sad J. Math. Vol. 36, No. 1, 2006, 11-19
Novi Sad J Math Vol 36, No 1, 2006, 11-19 FIXED POINT THEOREMS IN D-METRIC SPACE THROUGH SEMI-COMPATIBILITY Bijendra Singh 1, Shobha Jain 2, Shishir Jain 3 Abstract The objective of this paper is to introduce
More informationA note on a construction of J. F. Feinstein
STUDIA MATHEMATICA 169 (1) (2005) A note on a construction of J. F. Feinstein by M. J. Heath (Nottingham) Abstract. In [6] J. F. Feinstein constructed a compact plane set X such that R(X), the uniform
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 informationA fixed point theorem for weakly Zamfirescu mappings
A fixed point theorem for weakly Zamfirescu mappings David Ariza-Ruiz Dept. Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain Antonio Jiménez-Melado Dept.
More informationSOLUTION OF AN INITIAL-VALUE PROBLEM FOR PARABOLIC EQUATIONS VIA MONOTONE OPERATOR METHODS
Electronic Journal of Differential Equations, Vol. 214 (214), No. 225, pp. 1 1. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SOLUTION OF AN INITIAL-VALUE
More informationCommon fixed points of two maps in cone metric spaces
Rendiconti del Circolo Matematico di Palermo 57, 433 441 (2008) DOI: 10.1007/s12215-008-0032-5 Akbar Azam Muhammad Arshad Ismat Beg Common fixed points of two maps in cone metric spaces Received: July
More informationA fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces
Mathematica Moravica Vol. 21, No. 1 (2017), 37 50 A fixed point theorem for (µ, ψ)-generalized f-weakly contractive mappings in partially ordered 2-metric spaces Nguyen Trung Hieu and Huynh Ngoc Cam Abstract.
More informationCommon fixed point theorems for four self maps on a fuzzy metric space, satisfying common E. A. property
Available online at www.pelagiaresearchlibrary.com Avances in Applie Science Research, 2015, 6(10): 35-39 ISSN: 0976-8610 CDEN (SA): AASRFC Common fixe point theorems for four self maps on a fuzzy metric
More informationA fixed point theorem for w-distance
A fixed point theorem for w-distance A. Razani, Z. Mazlumi Nezhad and M. Boujary Abstract. In this paper, a fixed point theorem for a (Φ, Ψ, p)-contractive map on a complete metric space is proved. In
More informationCOMMON FIXED POINT THEOREM FOR FOUR MAPPINGS IN INTUITIONISTIC FUZZY METRIC SPACE USING ABSORBING MAPS
www.arpapress.com/volumes/vol10issue2/ijrras_10_2_12.pdf COMMON FIXED POINT THEOREM FOR FOUR MAPPINGS IN INTUITIONISTIC FUZZY METRIC SPACE USING ABSORBING MAPS Mona Verma 1 & R. S. Chandel 2 1 Technocrats
More informationA FIXED POINT THEOREM FOR MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE
IJMMS 29:9 (22) 531 536 PII. S161171227524 http://ijmms.hindawi.com Hindawi Publishing Corp. A FIXED POINT THEOREM FOR MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE A. BRANCIARI
More informationCommon Fixed Point Theorems for Generalized (ψ, φ)-type Contactive Mappings on Metric Spaces
Applied Mathematical Sciences, Vol. 7, 2013, no. 75, 3703-3713 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2013.35273 Common Fixed Point Theorems for Generalized (ψ, φ)-type Contactive
More informationCommon Fixed Point Theorems for Generalisation of R-Weak Commutativity
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728,p-ISSN: 2319-765X, Volume 8, Issue 4 (Sep. - Oct. 2013), PP 09-13 Common Fixed Point Theorems for Generalisation of R-Weak Commutativity T. R. Vijayan,
More informationResearch Article Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID 746045, 15 pages doi:10.1155/2010/746045 Research Article Common Fixed Points of Weakly Contractive and Strongly
More informationSOME FIXED POINT THEOREMS FOR ORDERED REICH TYPE CONTRACTIONS IN CONE RECTANGULAR METRIC SPACES
Acta Math. Univ. Comenianae Vol. LXXXII, 2 (2013), pp. 165 175 165 SOME FIXED POINT THEOREMS FOR ORDERED REICH TYPE CONTRACTIONS IN CONE RECTANGULAR METRIC SPACES S. K. MALHOTRA, S. SHUKLA and R. SEN Abstract.
More informationFIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE
www.arpapress.com/volumes/vol10issue3/ijrras_10_3_11.pdf FIXED POINT THEOREM USING COMPATIBILITY OF TYPE (A) AND WEAK COMPATIBILITY IN MENGER SPACE Bijendra Singh 1, Arihant Jain 2 and Javaid Ahmad Shah
More informationA Common Fixed Point Theorem for Self Mappings for Compatible Mappings of Type (E) in Fuzzy Metric space
Advances in Fuzzy Mathematics. ISSN 0973-533X Volume 11, Number 1 (2016), pp. 79-87 Research India Publications http://www.ripublication.com A Common Fixed Point Theorem for Self Mappings for Compatible
More informationCOMPLEX VALUED DISLOCATED METRIC SPACES. Ozgur Ege and Ismet Karaca
Korean J. Math. 26 (2018), No. 4, pp. 809 822 https://doi.org/10.11568/kjm.2018.26.4.809 COMPLEX VALUED DISLOCATED METRIC SPACES Ozgur Ege and Ismet Karaca Abstract. In this paper, we introduce complex
More informationBEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES
Kragujevac Journal of Mathematics Volume 44(3) (2020), Pages 401 413. BEST PROXIMITY POINT RESULTS VIA SIMULATION FUNCTIONS IN METRIC-LIKE SPACES G. V. V. J. RAO 1, H. K. NASHINE 2, AND Z. KADELBURG 3
More informationFunctional Analysis, Math 7320 Lecture Notes from August taken by Yaofeng Su
Functional Analysis, Math 7320 Lecture Notes from August 30 2016 taken by Yaofeng Su 1 Essentials of Topology 1.1 Continuity Next we recall a stronger notion of continuity: 1.1.1 Definition. Let (X, d
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 information