CONVERGENCE OF GENERALIZED \varphi-WEAK CONTRACTION MAPPING IN CONVEX METRIC SPACES

2017 ◽  
Vol 101 (7) ◽  
pp. 1437-1447
Author(s):  
Kyung Soo Kim ◽  
Huimin Lee ◽  
Se Jun Park ◽  
Seung Yeop Yu ◽  
Jaeh Hyeun Ahn ◽  
...  
2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Mihai Postolache

We introduce the concepts of a -weak contraction mapping of types and and we establish some fixed point theorems for a -weak contraction mapping of types and in complete -metric spaces. Our results generalize several well-known comparable results in the literature.


Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1505-1516 ◽  
Author(s):  
Binayak Choudhury ◽  
A. Kundu ◽  
N. Metiya

Partial metric spaces are generalizations of metric spaces which allow for non-zero self-distances. The need for such a definition was felt in the domain of computer science. Fixed point theory has rapidly developed on this space in recent times. Here we define a Ciric type weak contraction mapping with the help of discontinuous control functions and show that in a complete metric space such a function has a fixed point. Our main result has several corollaries and is supported with examples. One of the examples shows that the corollaries are properly contained in the theorem. We give applications of our results in partial metric spaces.


Author(s):  
Reena Jain

In this paper, the concept of generalized weak contraction mapping in the setting of generating space of [Formula: see text]-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.


Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6185-6203 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Poom Kumam

The purpose of this article is to prove some coincidence point and approximate solution method for generalized weak contraction mapping in b??metric spaces by using the concept of b-generalized pseudodistance. Also, we give some examples to illustrate our main results.


Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3875-3883
Author(s):  
Ljubomir Ciric ◽  
Sumit Chandok ◽  
Mujahid Abbas

Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243] extended the concept of F- contraction mapping introduced in [21], to two mappings. The aim of this paper is to introduce the notion of a generalized F1- weak contraction mapping and to study sufficient conditions for the existence of common fixed points for such class of mappings. As applications, related invariant approximation results are derived. The results obtained herein unify, generalize and complement various known results in the literature.


Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.


2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.


2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.


Sign in / Sign up

Export Citation Format

Share Document