Fixed Point and Common Fixed Point of Enriched Hardy-Rogers Contractions in Some Banach Spaces

Abstract In this paper, we prove some fixed point and common fixed point theorems for enriched contractions. Having in mind, the wide range of applicability of Banach contraction principle, the focus of this paper is to give more robust contractive conditions called enriched {{Hardy-Rogers contractions}}. Our results generalize and extend results of [Banach, S. (1922); Sur les Operations dans les Ensembles Abstraits et leur Appliication aux quations intrales, Fundamenta Mathematicae 3, 133-181], [Jungck G. (1976): Commuting mappings and fixed points, Amer. Math. Monthly, 83, 261-263], [Hardy G.E. and Rogers T.D.(1973), A generalization of a fixed point theorem of Reich, Canad.Math.Bull., 16, 201-206], [Berinde, V., Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22, 38 (2020). https://doi.org/10.1007/s11784-020-0769-9] and many more related results in the literature.