Fixed point theory in multiplicative metric space and its application in boundary value problems and cyclic mappings

Abstract

In this paper, building on the recent work of Stojan Radenović and Bessem Samet, we establish several fixed point theorems in multiplicative metric spaces for Jaggi-type and weak contractions. These results are derived using a function \(\varphi: [1, \infty) \to [0, \infty)\) satisfying \(\varphi(s) \ge b (\ln s)^c\) for \(s > 1\), with \(b\) and \(c\) positive constants. The theorems presented here are not equivalent to their classical analogues in standard metric spaces. To demonstrate the applicability of our results, we provide an example involving a boundary value problem for a second-order differential equation and the determination of a unique fixed point for a cyclic mapping.