Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces

Abstract

In this paper, new classes of rational Geraghty contractive mappings in the setup of b-metric spaces are introduced. Moreover, the existence of some fixed point for such mappings in ordered b-metric spaces are investigated. Also, some examples are provided to illustrate the results presented herein. Finally, an application of the main result is given.for all x, y, z ∈ X.In this case, the pair (X, d) is called a b-metric space.The following example (corrected from []) illustrates that a b-metric need not be a continuous function.if one of m, n is even and the other is even or ∞, , if one of m, n is odd and the other is odd (and m = n) or ∞, , otherwise.

On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces

“…Since then, several papers dealt with fixed point theory for single-valued and multi-valued operators in b-metric spaces (see, e.g., [7,9,12,13,17,19,21]). Definition 1.1.…”

“…For some useful examples of b-metric spaces, the reader may refer to [3,7,9,12,14,17,19,21]. Also, the notions such as b-convergent sequence, b-Cauchy sequence and b-complete space are defined by an obvious way.…”

“…Recently, many researchers have focused on different contractive conditions in complete metric and b-metric spaces endowed with a partial order and obtained many fixed point results in such spaces. For more details on fixed point results in ordered metric and ordered b -metric spaces, we refer the reader to [1,3,15,16,17,19,20,21]. Definition 2.1.…”

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

“…Following these initial papers, the existence and the uniqueness of (common) fixed points for the classes of both singlevalued and multivalued operators in the setting of (generalized) b-metric spaces have been investigated extensively, (see e.g. [1,3,4,5,9,13,14,15,16,24,26,27] and related references therein. )…”

A New Class of Contraction inb-Metric Spaces and Applications

“…In this interesting paper, Czerwik [1] generalized the Banach contraction principle in the context of complete b-metric spaces. After that many researchers reported the existence and uniqueness of fixed points of various operators in the setting of b-metric spaces (see, e.g., [2][3][4][5][6][7][8][9][10][11][12][13] and some references therein).…”