Fixed points of enriched contraction mappings in 2-normed spaces

TL;DR

This paper extends fixed point theorems for enriched contraction mappings from Banach spaces to 2-normed spaces, broadening the applicability of these mathematical principles.

Contribution

It introduces fixed point theorems for enriched contractions specifically in 2-normed spaces, generalizing prior results from Banach spaces.

Findings

Established fixed point existence in 2-normed spaces for enriched contractions.

Extended Banach contraction principles to a broader mathematical setting.

Provided new conditions under which fixed points can be guaranteed.

Abstract

Very recently, Berinde and P\u{a}curar obtained in [V. Berinde and M. P\u{a}curar, Approximating fixed points of enriched contractions in Banach spaces. Journal of Fixed Point Theory and Applications. \textbf{22}(2) (2020), 1--10.] an interesting generalization of the Banach contractive mapping principle in the framework of Banach spaces. The aim of this paper is to prove some fixed point theorems which extend the results of Berinde and P\u{a}curar to the case of 2-normed spaces.