Some Generalizations of Banach'S Contraction Principle Via Hermite–Hadamard Inequalities

This work is concerned with the study of existence and uniqueness of fixed points for some classes of single‐valued mappings defined on a complete metric space and satisfying new types of contractions involving convex or concave functions. Making use of Hermite–Hadamard inequalities, we establish two fixed point theorems for the considered classes of mappings. Our obtained results recover the Banach fixed point theorem. An example is provided, where our approach can be used, while the Banach fixed point theorem is inapplicable.