Introducing new controlled S-metric spaces, this paper investigates fixed point results for α-F contractions, suggesting significant implications.
In this paper, we introduce the concept of a new Controlled S-Metric type Space (CSMS) by using a function in the right hand side of the triangle inequality of S-metric space. The triangle inequality in the new CSMS will have the form Further, we provide some non-trivial examples, investigate (α, F)-contraction and prove several fixed point results in the setting of new CSMS. Furthermore, we present some of its consequences to illustrate the significance of our results. At the end, we provide an application to support the main result.
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Shereen et al. (2025) studied this question.
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