EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES

Abstract

Abstract. In this paper, we introduce the notion of generalized α − ψ-Geraghty multivalued mappings and investigate the existence of a fixed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.

A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces

“…On the other hand, this concept became popular after the interesting papers of Bakhtin [3] and Czerwik [4]. For more details in b-metric space and advances in fixed point theory in the setting of b-metric spaces, we refer e.g., [5][6][7][8][9][10][11][12][13][14][15][16][17]. Definition 1.…”

Fisher-Type Fixed Point Results in b-Metric Spaces

“…Among all, in 1993, Czerwik [6] suggested a successful and proper generalization of the metric space notion by introducing the concept of b-metric space. Following this famous result in the setting of b-metric spaces, several extensions in distinct aspects have been released in this direction (see e.g., [7][8][9][10][11][12][13][14][15] and references therein). In this paper, we study certain common fixed-point theorems for three maps in the setting of complete b-metric spaces.…”

Non-Unique Fixed Point Results in Extended B-Metric Space

“…One interesting generalization of metric space is b-metric space, formulated recently by Czerwik [1]. Following this result on b-metric space, several authors have reported a number of fixed point results in the framework of b-metric space (see, e.g., [2][3][4][5][6][7][8][9] and related references therein).…”