2023
DOI: 10.3390/sym15051100
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Controlled S-Metric-Type Spaces and Applications to Fractional Integrals

Nilay Ekiz Yazici,
Ozgur Ege,
Nabil Mlaiki
et al.

Abstract: In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann–Liouville fractional integrals and Atangana–Baleanu fractional integrals.

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Cited by 2 publications
(4 citation statements)
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“…(ii) A bipolar pseudo-metric (BPSM) is one where d is a bipolar pseudo-semi metric meeting (4). (iii) A bipolar metric is a BPSM d satisfying (2).…”
Section: Definition 1 ([3]mentioning
confidence: 99%
See 2 more Smart Citations
“…(ii) A bipolar pseudo-metric (BPSM) is one where d is a bipolar pseudo-semi metric meeting (4). (iii) A bipolar metric is a BPSM d satisfying (2).…”
Section: Definition 1 ([3]mentioning
confidence: 99%
“…and the set of edges given by the following: (1,3), (1,4), (1,5), (1,7), (1,13), (1,15), (3,2), (2,4), (5,2), (2, 7), (13,2), (2,15), (3,4), (3,5), (3,7), (3,13), (3,15), (5,4), (4,7), (13,4), (4,15), (5,7), (5,13), (5,15), (7,13), (7,15), (13,15).…”
Section: Graphical Bipolar B-mssmentioning
confidence: 99%
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“…Some researchers generalize the Banach principle by changing the type of contraction and adding conditions that satisfy the existence of a fixed point, like Karman et al [6], who established the notion of extended b-metric space and proved some fixed-point theorems in extended b-metric space. In recent years, there have been several important fixed-point results for some contractions in extended S-metric spaces and S b -metric spaces; see [7][8][9][10][11]. This paper aims to investigate a generalization of S-metric space, called extended S-metric space of type (α, β).…”
Section: Introductionmentioning
confidence: 99%