Abstract
AbstractThis article discusses a more general contractive condition for a class of extended (p ≥ 2) -cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. If the space is uniformly convex and the subsets are non-empty, closed and convex, then all the iterates converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduces to a unique fixed point if all such subsets intersect.
Highlights
A general contractive condition of rational type has been proposed in [1,2] for a partially ordered metric space
The fixed point theory for Kannan’s mappings is extended in [4] by the use of a non-increasing function affecting to the contractive condition and the best constant to ensure that a fixed point is obtained
More recent investigation about cyclic selfmappings is being devoted to its characterization in partially ordered spaces and to the formal extension of the contractive condition through the use of more general strictly increasing functions of the distance between adjacent subsets
Summary
A general contractive condition of rational type has been proposed in [1,2] for a partially ordered metric space. The existence and uniqueness of best proximity points of p(≥ 2) -cyclic -contractive self-mappings in reflexive Banach spaces has been investigated in [29].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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
