Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25)

Abstract

Recently, S-metric spaces are introduced as a generalization of metric spaces. In this paper, we consider the relationships between of an S-metric space and a metric space, and give an example of an S-metric which does not generate a metric. Then, we introduce new contractive mappings on S-metric spaces and investigate relationships among them by counterexamples. In addition, we obtain new fixed point theorems on S-metric spaces.

New contractive conditions of integral type on complete S-metric spaces

“…We call the function S q defined in Lemma 2.3 (1) as the S-metric generated by the metric q: It can be found an example of an S-metric which is not generated by any metric in [4,9]. Now we give the following theorem.…”

“…Example 2.11 Let R be the complete S-metric space with the S-metric defined in Example 1 given in [9]. Let us define the self-mapping T : R !…”

“…On the other hand some generalizations of the wellknown Ć irić's and Nemytskii-Edelstein fixed-point theorems obtained on S-metric spaces via some new fixed point results (see [8,9,13,14] for more details).…”

“…Some fixed-point theorems have been given for selfmappings satisfying various contractive conditions on an Smetric space (see [4,6,8,9,13,14]). One of the important results among these studies is the Banach's contraction principle on a complete S-metric space.…”

S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

“…In the literature, there exist some examples of S-metric which is not generated by any metric (see [8] and [9] for more details). Therefore, it is important to study new fixedpoint theorems on S-metric spaces.…”