Fixed Point Theorems for Kannan Contractions and Weakly Contractive Mappings on a Modular Metric Space Endowed with a Graph

Abstract

Abstract. The notion of a modular metric spaces were introduced by Chistyakov [5,6]. Abdou and Khamsi [1] gave the analog of Banach contraction principle in modular metric spaces. More recently, Alfuraidan [3] gave generalization of Banach contraction principle on a modular metric space endowed with a graph which is the modular metric version of Jachymski [8] fixed point results.In this paper, we generalize and prove some fixed point results for Kannan contraction and weakly contractive mappings in a modular metric space endowed with a graph. The result of this paper is new and improving the previously known result in modular metric spaces endowed with a graph.

On p-h Points and Completeness Property of a Partial Metric Space

“…In this connection it should also be mentioned that before the introduction of partial metric spaces, there were other generalizations of metric spaces, most notably 2metric spaces and generalized metric spaces where fixed point theorems for contractive mappings had been investigated (see for example the work of Das et al [4,10] or Dey et al [17]. Again in [1,5,11] one finds several fixed point theorems proved for operators involving Kannan contractions, weak contractions and ground space sometimes endowed with an associated graph. In particular, exclusively with Kannan contraction in fixed point theory, we have references like [8,12,13].…”