Fixed Points Theorems for Generalised Weakly Contractive Mappings

Abstract

In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results.

Common fixed point for some generalized contractive mappings in a modular metric space with a graph

“…In [9], Rhoades extended a part of this study to an arbitrary Banach space. The notion of weak contraction has been studied by other authors in the setting of metric spaces (see [8,12] and the references therein). In [13], Zhang Theorem ( [13]) Let X be a complete metric space, and let T, S : X − → X be two selfmappings satisfying Then T and S have a unique common fixed point in X.…”

Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

“…It is widely used in many fields of mathematics. Due to its importance, many authors have generalized this result in various directions [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Ciric [1] introduced the concept of generalized contractions.…”