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http://dx.doi.org/10.7468/jksmeb.2022.29.1.1

COMMON n-TUPLED FIXED POINT THEOREM UNDER GENERALIZED MIZOGUCHI-TAKAHASHI CONTRACTION FOR HYBRID PAIR OF MAPPINGS  

Deshpande, Bhavana (Department of Mathematics, Govt. Arts and Science College)
Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)
Publication Information
The Pure and Applied Mathematics / v.29, no.1, 2022 , pp. 1-17 More about this Journal
Abstract
We establish a common n-tupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction. An example is given to validate our results. We improve, extend and generalize several known results.
Keywords
generalized Mizoguchi-Takahashi contraction; n-tupled fixed point; n-tupled coincidence point; w-compatibility; F-weakly commuting;
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1 A. Amini-Harandi & D. O'Regan: Fixed point theorems for set-valued contraction type mappings in metric spaces. Fixed Point Theory Appl. 2010, 7 (2010). Article ID 390183.
2 T.G. Bhaskar & V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), no. 7, 1379-1393.   DOI
3 S. Banach: Sur les Operations dans les Ensembles Abstraits et leur. Applications aux Equations Integrales, Fund. Math. 3 (1922), 133-181.   DOI
4 L. Ciric, B. Damjanovic, M. Jleli & B. Samet: Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications. Fixed Point Theory Appl. 2012, 51.
5 B. Deshpande: Common fixed point for set and single valued functions without continuity and compatibility. Math. Morav. 11 (2007), 27-38.   DOI
6 B. Deshpande & S. Chouhan: Fixed points for two hybrid pairs of mappings satisfying some weaker conditions on noncomplete metric spaces. Southeast Asian Bull. Math. 35 (2011), 851-858.
7 M. Imdad, A.H. Soliman, B.S. Choudhury & P. Das: On n-tupled coincidence point results in metric spaces. Journal of Operators Volume 2013, Article ID 532867, 8 pages.
8 B. Deshpande & A. Handa: Common n-tupled fixed point for hybrid pair of mappings under new contractive condition. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), no. 3, 165-181.
9 B. Deshpande & A. Handa, n-tupled coincidence and fixed point result for hybrid pair of mappings under generalized nonlinear contraction. Southeast Asian Bull. Math. 40 (2016), 655-670.
10 B. Deshpande & R. Pathak. Fixed point theorems for noncompatible discontinuous hybrid pairs of mappings on 2- metric spaces. Demonstr. Math. XLV 2012, no. 1, 143-154.
11 V. Lakshmikantham & L. Ciric: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70 (2009), no. 12, 4341-4349.   DOI
12 J.T. Markin: Continuous dependence of fixed point sets. Proc. Amer. Math. Soc. 38 (1947), 545-547.   DOI
13 S. Sharma & B. Deshpande. Fixed point theorems for set and single valued mappings without continuity and compatibility. Demonstr. Math. XL (2007), no. 3, 649-658.
14 S. Sharma & B. Deshpande: Compatible multivalued mappings satisfying an implicit relation. Southeast Asian Bull. Math. 30 (2006), 535-540.
15 W.S. Du: Coupled fixed point theorems for nonlinear contractions satisfied Mizoguchi-Takahashi's condition in quasi ordered metric spaces. Fixed Point Theory Appl. 2010, 9 (2010) Article ID 876372.
16 J. Harjani, B. Lopez & K. Sadarangani: Fixed point theorems for mixed monotone operators and applications to integral equations. Nonlinear Anal. 74 (2011), 1749-1760.   DOI
17 I. Kubiaczyk & B. Deshpande: A common fixed point theorem for multivalued mappings through T-weak commutativity. Math. Morav. 10 (2006), 55-60.
18 I. Kubiaczyk & B. Deshpande: Common fixed point of multivalued mappings without continuity. Fasc. Mathe. 37 (2007), no. 9, 19-26.
19 S.B. Nadler: Multivalued contraction mappings. Pacific J. Math. 30 (1969), 475-488.   DOI
20 J. Rodriguez-Lopez & S. Romaguera: The Hausdorff fuzzy metric on compact sets. Fuzzy Sets Syst. 147 (2004), 273-283.   DOI
21 I. Kubiaczyk & B. Deshpande: Noncompatibility, discontinuity in consideration of common fixed point of set and single valued mappings. Southeast Asian Bull. Math. 32 (2008), 467-474.
22 N. Mizoguchi & W. Takahashi: Fixed point theorems for multivalued mappings on complete metric spaces. J. Math. Anal. Appl. 141 (1989), 177-188.   DOI