Certain Fixed Point Results for (α-F)-Contraction in New Controlled S-Metric Type Spaces (Contemporary Mathematics, 2025)
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.
Keywords: fixed poin; S-metric-type space; controlled function; integral equations