On the extended multivalued Geraghty type contractions

Volume 9, Issue 6, pp 4695--4706 http://dx.doi.org/10.22436/jnsa.009.06.108

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Authors

Hojjat Afshari - Faculty of Basic Science, University of Bonab, Bonab, Iran. Hamed H. Alsulami - Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia. Erdal Karapinar - Department of Mathematics, Atilim University, 06836, Incek, Ankara, Turkey.

Abstract

In this paper we present some absolute retract results for modified Geraghty multivalued type contractions in b-metric space. Our results, generalize several existing results in the corresponding literature. We also present some examples to support the obtained results.

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Keywords

• Fixed points
• extended multivalued Geraghty type contractions.

MSC

•  46T99
•  47H10
•  54H25

References

• [1] H. Afshari, Sh. Rezapour, Absolute retractivity of some sets to two-variables multifunctions, Anal. Theory Appl., 28 (2012), 73--78


• [2] H. Afshari, Sh. Rezapour, N. Shahzad, Absolute retractivity of the common fixed points set of two multifunctions, Topol. Methods Nonlinear Anal., 40 (2012), 429--436


• [3] H. Afshari, Sh. Rezapour, N. Shahzad, Some results on absolute retractivity of the fixed points set of KS- multifunctions, Math. Slovaca, 65 (2015), 1509--1516


• [4] M. C. Alicu, O. Mark, Some properties of the fixed points set for multifunctions, Studia Univ. Babe-Bolyai Math., 25 (1980), 77--79


• [5] H. Aydi, M. F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak \(\phi\)-contractions on b-metric spaces, Fixed Point Theory, 13 (2012), 337--346


• [6] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5--11


• [7] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263--276


• [8] M. Kikkawa,T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69 (2008), 2942--2949


• [9] M. Kikkawa,T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory and Appl., 2008 (2008), 8 pages


• [10] B. Ricceri, Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque á valeurs convexes (French), Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 81 (1987), 283--286


• [11] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165


• [12] H. Schirmer, Properties of the fixed point set of contractive multifunctions, Canad. Math. Bull., 13 (1970), 169--173


• [13] A. Sîntămărian, A topological property of the common fixed points set of two multivalued operators satisfying a Latif-Beg type condition, Fixed Point Theory, 9 (2008), 561--573


• [14] A. Sîntămărian, A topological property of the common fixed points set of two multivalued operators, Nonlinear Anal., 70 (2009), 452--456


• [15] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861--1869


• [16] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., 340 (2008), 1088--1095