scholarly journals The Convex (\delta,L) Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language

Author(s):  
Clement Boateng Ampadu

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.

Author(s):  
Clement Boateng Ampadu

In this paper we introduce the multiplicative version of cone-C class functions [1], and obtain some contraction mapping theorems of the Hardy and Rogers kind in multiplicative cone metric space endowed with such functions. Further, we propose some open problems that are publishable in nature.


2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Joseph Frank Gordon

In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.


1977 ◽  
Vol 17 (3) ◽  
pp. 375-389 ◽  
Author(s):  
Walter D. Neumann

It is shown how George D. Birkhoff's proof of the Poincaré Birkhoff theorem can be modified using ideas of H. Poincaré to give a rather precise lower bound on the number of components of the set of periodic points of the annulus. Some open problems related to this theorem are discussed.


2017 ◽  
Vol 9 (2) ◽  
pp. 1
Author(s):  
Sagita Charolina Sihombing ◽  
Ety Septiati

In this paper, we study the existence of fixed point of the φ-weak contraction mapping in the complete partial metric space for multivalued mapping. Distance calculations are performed using Hausdorff metric. The result obtained in this paper is an extension of similar result for single valued mapping.


2014 ◽  
Vol 47 (1) ◽  
Author(s):  
D. Wardowski ◽  
N. Van Dung

AbstractIn this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature


2019 ◽  
Vol 24 (2) ◽  
pp. 88
Author(s):  
Rifaat Saad Abdul-Jabbar

In this paper, a fixed point theorem under F-contraction mapping was considered and proved in complete quasi-metric space. This theorem was considered by Piri and Kumam in [1]. Subject Classification : 30C45; 30C10; 47B38    http://dx.doi.org/10.25130/tjps.24.2019.037


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