Coincidence point theorem for a new type of contraction on metric spaces

Abstract

In this article, we introduce a new type of contraction and prove a coincidence point theorem which generalizes some known results in this area. The artile includes examples which show the validity of our result and that these contractions form a superclass of many classes of contractions known in the litrature.

On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

“…Motivated by the above, the aim of this paper is to establish the existence and uniqueness of coincidence and common fixed point of eight self-maps in a (noncomplete) metric spaces satisfying a new type contraction condition, called F M -contraction via common (CLR (AB)(ST ) ) property or common property (E.A.). Our results generalize, extend and improve the results of Wardowski [22], Batra et al [2], Tomar et al [19] and others existing in the literature (for instance, Chatterjea [3], Cosentino and Vetro [4],Ćirić [5], Kannan [8], Reich [12], Wardowski and Dung [23], Roldan and Sintunavarat [13] and references therein) without using completeness or closedness of subspace/space or containment requirement of range space of involved maps or continuity of involved maps. Moreover, the new type F M -contraction defined by us is more comprehensive than the one introduced by Piri and Kumam [11] and Wardowski [22].…”

“…If H is continuous then, clearly, H(t) = t. The uniqueness of the fixed point results easily from (2).…”

“…Moreover, the maps are discontinuous even at the common fixed point. Whereas, Batra et al [2] established coincidence point of a pair of self-maps by taking containment of range space of involved maps, completeness of space along with continuity and commutativity of both maps. The weak compatibility used here is indeed weaker than the commutativity of a pair of maps.…”

Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

“…The reader interested in fixed points results obtained employing the concept of F-contraction is referred to [19][20][21][22][23][24][25][26][27][28][29][30][31]. In this paper, we proved that some of the conditions in Theorems 2-4 are superfluous.…”

On F-Contractions: A Survey

“…Bashir et al [31], extend Wardowski's idea of F-contraction by introducing the reversed generalized F-contraction mapping. Further generalizations are F ωcontractions [32], F-g-contractions [33], F-contractive mappings of Hardy-Rogers-type [34,35]. In [36] the notion of dynamic process for generalized F-contraction mappings is introduced.…”