Prešić Type Nonself Operators and Related Best Proximity Results

Muhammad Usman Ali,Misbah Farheen,Tayyab Kamran,Georgeta Maniu

doi:10.3390/math7050394

Abstract

The purpose of this article is to discuss the existence of best proximity points for Pre s ˇ i c ´ -type nonself operators, say T : A k → B . We also give several examples to support our results. As a consequence of our results, we have provided some interesting formulations of Pre s ˇ i c ´ fixed point results.

Highlights

Introduction and PreliminariesThe kth order nonlinear difference equation is of the form:x n + k = T ( x n, x n +1, . . . , x n + k −1 ) (1)where T is a continuous function from I k ⊂ Rk into I ⊂ R
The kth order nonlinear difference equation is of the form: x n + k = T ( x n, x n +1, . . . , x n + k −1 )
The existence of the equilibrium point of a certain difference equation is of interest and has been extensively discussed in the literature; see for example Prešić [1]

Summary

Introduction

The existence of the equilibrium point of a certain difference equation is of interest and has been extensively discussed in the literature; see for example Prešić [1]. In the literature of fixed point theory, the result of Prešić [1] is considered as one of the most important extensions of the Banach contraction principle for the operators defined on product spaces. This famous extension [1] was stated as: Let ( X, d) be a complete metric space, k be a positive integer, and T : X k → X be a mapping such that:

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Results

Conclusion