Abstract
In this paper, we derive a best proximity point theorem for non-self-mappings satisfied proximal cyclic contraction in PM-spaces and this shows the existence of optimal approximate solutions of certain simultaneous fixed point equations in the event that there is no solution. As an application we consider a nonlinear programming problem. Our results extend and improve the recent results of (Sadiq Basha in Nonlinear Anal. 74(17):5844-5850, 2011).
Highlights
Best proximity point theorems are those results that provide sufficient conditions for the existence of a best proximity point and algorithms for finding best proximity points
It is interesting to note that best proximity point theorems generalized fixed point theorems in a natural fashion
A mapping S : A → B is said to be a proximal contraction of the first kind if there exists a non-negative number α < such that
Summary
Best proximity point theorems are those results that provide sufficient conditions for the existence of a best proximity point and algorithms for finding best proximity points. Given nonempty closed subsets A and B of a complete PM-space (X, F, ∗), a contraction non-self-mapping T : A → B does not necessarily has a fixed point. ( ) A PM-space (X, F, ∗) is said to be complete if and only if every Cauchy sequence in X is convergent to a point in X.
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
