Pair $(Q,h)$ on Some Fixed Point Theorems for $\alpha$-Admissible Mappings in $S$-Metric Spaces

Hojjat Ansari, Arsalan; Nazari, Alimohammad; Taati, Mohammad

doi:‎10.22034/maco.6.1.6

Pair $(Q,h)$ on Some Fixed Point Theorems for $\alpha$-Admissible Mappings in $S$-Metric Spaces

Articles in Press

Document Type : Original Article

Authors

Arsalan Hojjat Ansari ¹ ^¶

Alimohammad Nazari ²

Mohammad Taati ³

¹ Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

² Department of Mathematics, Arak University, P.O. Box 8349-8-38156, Arak, Iran.

³ Department of Mathematics, Payame Noor University, Tehran, Iran.

‎10.22034/maco.6.1.6

Abstract

In this paper, we introduce a novel class of contraction mappings defined on $S$-metric spaces. Our approach relies on the concept of $\alpha$-admissible mappings and the newly defined notion of upper class pairs of type III. We prove a generalized fixed point theorem that extends and unifies several existing results in the literature, most notably the theorems of Shimpi and Dapke \cite{dap}. The main result is formulated in terms of a pair $(Q,h)$, where $h$ belongs to a subclass of type III and $Q$ satisfies appropriate conditions. By choosing specific forms for $h$ and $Q$, we obtain a series of corollaries that encompass well-known fixed point theorems as particular cases. The findings not only enhance the applicability of fixed point theory in $S$-metric spaces but also establish a unified framework for future research in this area.

Keywords

Fixed point

$S$-metric

upper class of type III

Subjects