Kantorovich’s Fixed Point Theorem and Coincidence Point Theorems for Mappings in Vector Metric Spaces

2021 ◽  
Author(s):  
Aram V. Arutyunov ◽  
Evgeny S. Zhukovskiy ◽  
Sergey E. Zhukovskiy ◽  
Zukhra T. Zhukovskaya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point

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 A Tripled Fixed Point Theorem in C ∗ -Algebra-Valued Metric Spaces and Application in Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Vahid Parvaneh ◽  
Samira Hadi Bonab ◽  
Hasan Hosseinzadeh ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Tripled Fixed Point ◽  
C Algebra

Our aim is to establish a tripled fixed and coincidence point result on generalized C ∗ -algebra-valued metric spaces. We present an example on matrices. At the end, we give an application on integral equations.

Fixed Point Theorems for Compatible Mappings of Type (R) in 2-Metric Spaces

2015 ◽  
Vol 2 ◽  
pp. 17-27
Author(s):  
Oinam Budhichandra Singh ◽  
Th. Indubala ◽  
N. Leenthoi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Compatible Mappings

The aim of this paper is to introduce the concept of compatible mappings of type (R) in 2-metric spaces and to prove a coincidence point theorem and a fixed point theorem for compatible mappings of type (R) in 2-matric spaces.

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 Coincidence and Fixed Point of Nonexpansive Type Mappings in 2-Metric Spaces

2019 ◽  
pp. 191-206
Author(s):  
H. A. Hammad ◽  
A. H. Ansari ◽  
R. A. Rashwan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Type Condition

The aim of this paper is to prove a coincidence point theorem for a class of self mappings satisfying nonexpansive type condition under various conditions and a fixed point theorem is also obtained. Our results extend and generalize the corresponding result of Singh and Chandrashekhar [A fixed point theorem in a 2-metric space and an application, J. Natural and Physical Sci. 15(1-2) (2001), 55-64].

scholarly journals Unique Coincidence and Fixed Point Theorem forg-Weakly C-Contractive Mappings in Partial Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Saud M. Alsulami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces

We prove that every map satisfying theg-weakly C-contractive inequality in partial metric space has a unique coincidence point. Our results generalize several well-known existing results in the literature.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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