Abstract
AbstractThe aim of this paper is to introduce and study certain new concepts ofα-ψ-proximal contractions in an intuitionistic fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic fuzzy metric spaces. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain some recent fixed point theorems as special cases. Moreover, we discuss some illustrative examples to highlight the realized improvements.MSC:47H10, 54H25.
Highlights
1 Introduction Many problems arising in different areas of mathematics, such as optimization, variational analysis, and differential equations, can be modeled as fixed point equations of the form Tx = x
A best approximation theorem guarantees the existence of an approximate solution, a best proximity point theorem is contemplated for solving the problem to find an approximate solution which is optimal
If the mapping under consideration is a self-mapping, we note that this best proximity theorem reduces to a fixed point
Summary
Let A and B be nonempty subsets of an intuitionistic fuzzy metric space (X, M, N, ∗, ) and T : A → B be a non-self-mapping. Let T : A → B be a t-uniformly continuous non-self-mapping satisfying the following assertions: (i) T is an α-proximal admissible mapping and T(A (t)) ⊆ B (t) for all t > ; (ii) T is a α-ψ-proximal contractive mapping; (iii) for any sequence {yn} in B (t) and x ∈ A satisfying M(x, yn, t) → M(A, B, t) as n → +∞, x ∈ A (t) for all t > ; (iv) there exist elements x and x in A (t) such that
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
