Extensions of Ćirić and Wardowski type fixed point theorems in D-generalized metric spaces

Abstract

In this paper, we study an interesting generalization of standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces due to the recent work of Jleli and Samet. Here we modify the result forĆirić quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings. Moreover, we establish fixed point theorems for two well-known nonlinear contractions like rational contraction mappings and Wardowski type contraction mappings. Several important results in the literature can be derived from our results. Suitable examples are presented to substantiate our obtained results.

Fixed point results concerning α-F-contraction mappings in metric spaces

“…It is widely known that the Banach contraction principle [1] is the first metric fixed point theorem and one of the most powerful and versatile results in the field of functional analysis. Due to its significance and several applications, over the years, it has been generalized in different directions by several mathematicians (for example, see ( [2,3,4,5,7,10,17,18,15,16,19]) and references therein).…”

New fixed point results in orthogonal metric spaces with an application

“…On account of the fact that the metric fixed point theory plays a crucial role in solving many problems in different branches of science, many authors went into the possibility of altering the concepts of metric and metric spaces (see for examples, [3,7,8]). Lately, Gordji et al [4] coined an interesting notion of the orthogonal sets and then, orthogonal metric spaces.…”

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

“…For investigations in partial metric spaces, works of Valero and Oltra [9,15], Romaguera [16], Altun et al [6], Choudhury [2,3] are noteworthy. 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.…”