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
Related Articles
- EP ID EP470771
- DOI 10.34198/ejms.1219.157169
- Views 259
- Downloads 0
Fully Homomorphic Cipher Based on Finite Algebraic Structures
A way to increase the robustness of a cryptographic algorithm toward unauthorized inversion can be obtained through application of non-commutative or non-associative algebraic structures. In this regard, data security be...
A Note on the Notions of Topological Entropy
Topological entropy is used to determine the complexity of a dynamical system. This paper aims to serve as a stepping stone for the study of topological entropy. We review the notions of topological entropy, give an over...
On the Solution of Fractional Option Pricing Model by Convolution Theorem
The classical Black-Scholes equation driven by Brownian motion has no memory, therefore it is proper to replace the Brownian motion with fractional Brownian motion (FBM) which has long-memory due to the presence of the H...
Insertion of a Contra-continuous Function between Two Comparable Real-valued Functions
A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a contra-continuous function between two comparable real-valued functions on such topological spaces that kernel of sets are...
Strong Insertion of a Contra-$alpha$-continuous Function between Two Comparable Real-valued Functions
Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a contra-a-continuous function between two comparable real-valued functions.