\(F\)-convex contraction via admissible mapping and related fixed point theorems with an application (Q1634379)

Summary: In this paper, we introduce \(F\)-convex contraction via admissible mapping in the sense of \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)] which extends convex contraction mapping of type-2 of \textit{V. I. Istratescu} [Libertas Math. 1, 151--163 (1981; Zbl 0477.54032)] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.