Completeness Problem via Fixed Point Theory

Abstract

The purpose of this paper is to present the notion of MR-Kannan type contractions using the generalized averaged operator. Several examples are provided to illustrate the concept presented herein. We provide a characterisation of normed spaces using MR-Kannan type contractions with a fixed point. We investigate the Ulam–Hyers stability and well-posedness result for the mappings presented here.

Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

“…On the other hand, in 2023, Anjum et al [22] generalized Theorem 4 by introducing the concept of ( , a)-MR-Kannan type contraction. The principal outcome highlighted in [22] is presented as follows: Theorem 5 ([22]).…”

“…On the other hand, in 2023, Anjum et al [22] generalized Theorem 4 by introducing the concept of ( , a)-MR-Kannan type contraction. The principal outcome highlighted in [22] is presented as follows: Theorem 5 ([22]). Let (Θ, • ) be a Banach space and P : Θ → Θ be an ( , a)-MR-Kannan type contraction, that is an operator satisfying…”

“…Before proceeding with the proof of the main theorem of our paper, the following findings are required from [22].…”

“…where ∈ β is called a generalized averaged operator ( [22,23]). We would like to direct the reader's attention to the fact that the term generalized averaged operator refers to a specific type of admissible perturbations [23,24].…”