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.

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.

Ulam-Hyers stability theorem by tripled fixed point theorem

2016 ◽  
Vol 56 (1) ◽  
pp. 77-97
Author(s):  
Animesh Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Stability Theorem ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Vector Valued ◽  
Stability Results

AbstractThis paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

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 FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

2021 ◽  
pp. 237
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Urysohn Integral Equations ◽  
Complex Valued

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature.

scholarly journals A Common Fixed Point Theorem for Nonlinear Quasi-Contractions on b -Metric Spaces with Application in Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zoran D. Mitrović ◽  
Ivan D. Aranđelović ◽  
Vesna Mišić ◽  
Abdollah Dinmohammadi ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Comparison Functions ◽  
Nonlinear Comparison ◽  
Common Fixed Point Theorem

In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results.

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