In this paper, we introduce the concept of generalised S − β − ψ contractive type mappings. For these mappings we prove some fixed point theorems in the setting of S-metric space.
In this paper, we introduce the concept of generalised S − β − ψ contractive type mappings. For these mappings we prove some fixed point theorems in the setting of S-metric space.
“…Therefore, it is important to study new fixedpoint theorems on S-metric spaces. Some fixed-point results have been still investigated using different techniques to generalize some well-known fixed-point theorems (for example, see [10], [11], [12] and [13] for more details).…”
Section: S U V W = If and Only If U V W = = (S2) ( ) ( ) ( mentioning
Recently, some generalized metric spaces have been studied to obtain new fixed-point theorems. For example, the notion of S-metric space was introduced for this
“…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).…”
Section: Introductionmentioning
confidence: 98%
“…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.…”
An S-metric space is a three-dimensional generalization of a metric space. In this paper our aim is to examine some fixed-point theorems using new contractive conditions of integral type on a complete S-metric space. We give some illustrative examples to verify the obtained results. Our findings generalize some fixed-point results on a complete metric space and on a complete S-metric space. An application to the Fredholm integral equation is also obtained.
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