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 Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 852 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Unique Solution ◽  
Integral Equations ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Urysohn Integral Equations ◽  
Fixed Point Technique ◽  
Complex Valued

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. 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. Previous known related results in the literarure and some other known results in the literature.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
J. Harjani ◽  
B. López ◽  
K. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type

The purpose of this paper is to present a fixed point theorem using a contractive condition of rational type in the context of partially ordered metric spaces.

scholarly journals Fixed Point Theorems for Set-Valued Mappings under Contractive Condition in Quasi-Metric Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Mohseni Kolagar ◽  
Y.J. Cho ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Generalized Weak Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Set Valued Mappings ◽  
Weakly Contractive

Abstract In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

scholarly journals A Suzuki-type common fixed point theorem

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2951-2956
Author(s):  
N. Chandra ◽  
M.C. Arya ◽  
Mahesh Joshi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorem

In this paper we establish a common fixed point theorem for two maps under the generalized contractive condition in a complete metric spaces.

scholarly journals A common fixed point theorem using implicit relation and property (E.A) in metric spaces

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 211-234 ◽  
Author(s):  
H. Pathak ◽  
Rosana Rodriguez-López ◽  
R.K. Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Implicit Relation ◽  
Weak Compatibility ◽  
Common Fixed Point Theorem

In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

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