The Convex $(\delta,L)$ Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language
Journal Title: Earthline Journal of Mathematical Sciences - Year 2019, Vol 1, Issue 2
Abstract
Let $(X,d)$ be a metric space. A map $T:X \mapsto X$ is said to be a $(\delta,L)$ weak contraction [1] if there exists $\delta \in (0,1)$ and $L\geq 0$ such that the following inequality holds for all $x,y \in X$: $d(Tx,Ty)\leq \delta d (x,y)+Ld(y,Tx)$ On the other hand, the idea of convex contractions appeared in [2] and [3]. In the first part of this paper, motivated by [1]-[3], we introduce a concept of convex $(\delta,L)$ weak contraction, and obtain a fixed point theorem associated with this mapping. In the second part of this paper, we consider the map is a non-self map, and obtain a best proximity point theorem. Finally, we leave the reader with some open problems.
Authors and Affiliations
Clement Boateng Ampadu
Keywords
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- EP ID EP470771
- DOI 10.34198/ejms.1219.157169
- Views 271
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