Certain Fixed Point Results for (α-F)-Contraction in New Controlled S-Metric Type Spaces

Authors

Iqra Shereen Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
Ambreen Bano Department of Mathematics and Statistics, Ripha International University, Haj Complex I-14, Islamabad, 44220, Pakistan
Tayyab Kamran Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
Umar Ishtiaq Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan
Ioannis K. Argyros Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA https://orcid.org/0000-0002-9189-9298

DOI:

https://doi.org/10.37256/cm.6520255274

Keywords:

fixed poin, S-metric-type space, controlled function, integral equations

Abstract

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.