Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces

Abstract

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; P\u{a}curar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. We illustrate the obtained theoretical results by providing an example of an enriched contraction in a quasi-Banach space which is not a Banach space to show that our new results are effective generalizations of the previous ones in literature.