Fixed Point Results under Nonlinear Suzuki $(F,\mathcal{R}^{\neq})$-contractions with an Application

Abstract

In this article, we introduce the idea of nonlinear Suzuki $(F,\mathcal{R}^{\neq})$-contractions, which subsumes the contrctive conditions due to Suzuki [Nonlinear Anal. 71 (2009) 5313-5317] and Wardowski [Fixed Point Theory Appl. (2012) 94:6]. Utilizing our newly introduced contraction, we establish some relation-theoretic fixed point theorems. Furthermore, we adopt an example to the support of our newly proved results. In the end, we employ our main results to ascertain the existence of solution for nonlinear matrix equation.