Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces


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	Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces


	Fixed Point Theory, Volume 18, No. 1, 2017, 315-328, March 1st, 2017 DOI: 10.24193/fpt-ro.2017.1.25 Authors: Rale M. Nikolić, Siniša N. Ješić and Nataša A. Babačev Abstract: In this paper, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition in the sense of Fang [On φ-contractions in probabilistic and fuzzy metric spaces. Fuzzy Set Syst. (267) 2015, 86--99] will be proved, using the notion of strictly convex structure introduced by Ješić et al. [Ješić, S.N, Nikolić, R.M., Babačev N.A., A Common Fixed Point Theorem in Strictly Convex Menger PM-spaces, Filomat (28)(4) 2014, 735--743] for Menger PM-spaces. As a consequence of main result we will give probabilistic generalization of Assad and Kirk's result [Assad, N.A., Kirk, W.A., Fixed-point theorems for set-valued mappings of contractive type. Pacific J. Math. (43) 1972, 553--562]. Key Words and Phrases: Menger PM-spaces, strictly convex structure, fixed point, non-self mappings. 2010 Mathematics Subject Classification: 47H10, 54H25. Published on-line: March 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents