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 232
- Downloads 0
Further Generalized Beta Function with Three Parameters Mittag-Leffler Function
The purpose of the present paper is to introduce a new extension of extended Beta function by product of two Mittag-Leffler functions. Further, we present certain results including summation formulas, integral representa...
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...
The Convex $(\delta,L)$ Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language
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(...
The Number of Conjugacy Classes and Irreducible Characters in a Finite Group
In this paper, number of conjugacy classes and irreducible characters in a non-abelian group of order $2^6$ are investigated using cycle pattern of elements. Through the exploits of commutator and representation of elem...
Improved Perceptual Video Encryption Technique using Residue Number System
In this paper, we propose an enhanced perceptual video encryption technique to speed-up and secure cipher video transmitted across networks using Residue Number System (RNS). The technique proposes a new reverse converte...