scholarly journals New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Existence Theorems ◽  
Coupled Fixed Point ◽  
Point Property ◽  
Coincidence Points ◽  
Approximate Fixed Point Property

Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. Moreover, some applications of our results to the existence of coupled coincidence point and coupled fixed point are also presented.

scholarly journals New Results and Generalizations for Approximate Fixed Point Property and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Farshid Khojasteh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Nadler’S Fixed Point Theorem ◽  
Approximate Fixed Point Property

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions andα-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.

scholarly journals The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Generalized Contraction ◽  
Common Fixed Point Theorems

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

scholarly journals On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Fixed Point Properties ◽  
Contractive Maps

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

scholarly journals Some new coincidence point results for single-valued and multi-valued mappings in $b$-metric spaces via digraphs

2020 ◽  
Vol 53 (1) ◽  
pp. 69-84
Author(s):  
S. K. Mohanta ◽  
R. Kar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Nadler’S Fixed Point Theorem

We introduce the concept of generalized $F$-$G$-contraction and prove some new coincidence point results for single-valued and multi-valued mappings in $b$-metric spaces endowed with a digraph $G$. Our results generalize and extend several well-known comparable results including Nadler's fixed point theorem for multi-valued mappings. Moreover, we give some examples to justify the validity of our main result.

scholarly journals Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zorana Golubović ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Partial Metric ◽  
Coincidence Points ◽  
Coupled Coincidence Points ◽  
Partial Metric Spaces ◽  
Coupled Coincidence

New coupled coincidence point and coupled fixed point results in ordered partial metric spaces under the contractive conditions of Geraghty, Rakotch, and Branciari types are obtained. Examples show that these results are distinct from the known ones.

scholarly journals Types of Fixed Points of Set-Valued Contraction Mappings for Comparable Elements

2020 ◽  
pp. 190-195
Author(s):  
Shaimia Qais Latif ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Contraction Mappings ◽  
Coupled Fixed Point Theorem ◽  
Contraction Condition

This paper is concerned with the study of the fixed points of set-valued contractions on ordered metric spaces. The first part of the paper deals with the existence of fixed points for these mappings where the contraction condition is assumed for comparable variables. A coupled fixed point theorem is also established in the second part.

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