scholarly journals Some results on complex valued metric spaces employing an implicit relation with complex coefficients and its applications

2018 ◽  
Vol 36 (3) ◽  
pp. 103-113 ◽  
Author(s):  
Fayyaz Rouzkard
Keyword(s):  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Coefficient ◽  
Implicit Relation ◽  
Weakly Compatible ◽  
Contraction Condition ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Complex Coefficients ◽  
Common Fixed Point Theorems

In this paper, we establish coincidence point and common fixed point theorems involving two pairs of weakly compatible mapping satisfying contraction condition with complex coefficient are proved in complex valued metric space. The presented theorems generalize, extend and improve many existing results in the literature. An example is given at the end of the paper.

scholarly journals Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

2019 ◽  
Vol 38 (4) ◽  
pp. 9-29
Author(s):  
Waleed Mohd Alfaqih ◽  
Mohammad Imdad ◽  
Fayyaz Rouzkard
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Relation ◽  
Common Solution ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

The purpose of this paper is to prove some common fixed point theorems for two pairs of weakly compatible mappings in complex valued metric spaces satisfying an implicit relation. Several illustrative examples are given which demonstrate the usefulness of our utilized implicit relation. Beside generalizing and improving several well known core results of the existing literature we can deduce several new contractions which have not obtained before in complex valued metric spaces. As an application of our results, we prove the existence and uniqueness of common solution of Hammerstein as well as Urysohn integral equations.

scholarly journals Common Fixed Point Results for Six Mappings via Integral Contractions with Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Mian Bahadur Zada ◽  
Muhammad Sarwar ◽  
Nayyar Mehmood
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Inequality ◽  
Dynamical Programming ◽  
System Of Functional Equations ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Common fixed point theorems for six self-mappings under integral type inequality satisfying (E.A) and (CLR) properties in the context of complex valued metric space (not necessarily complete) are established. The derived results are new even for ordinary metric spaces. We prove existence result for optimal unique solution of the system of functional equations used in dynamical programming with complex domain.

scholarly journals Weakly compatible maps in complex valued metric spaces and an application to solve Urysohn integral equation

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2695-2709
Author(s):  
Manoj Kumar ◽  
Pankaj Kumar ◽  
Sanjay Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality. Also, we prove common fixed point theorems for weakly compatible maps, weakly compatible along with (CLR) and E.A. properties that generalizes the results of Sintunavarat et al. [15]. Further, we apply our results to find the solution of Urysohn integral equations x(t) = ?b,a K1(t,s,x(s))ds + g(t), x(t) = ?b,a K2(t,s,x(s))ds + h(t), where t ? [a,b]? R,x,g,h ? X and K1,K2: [a,b] x [a,b] x Rn ? Rn.

scholarly journals Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jamshaid Ahmad ◽  
Chakkrid Klin-Eam ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

scholarly journals Common Fixed Points Technique for Existence of a Solution of Urysohn Type Integral Equations System in Complex Valued b-Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 400
Author(s):  
Muhammad Suhail Aslam ◽  
Monica Felicia Bota ◽  
Mohammad S. R. Chowdhury ◽  
Liliana Guran ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Existence Of A Solution ◽  
Contraction Condition ◽  
Type Integral ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given.

scholarly journals COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLEX VALUED b-METRIC SPACES

2017 ◽  
Vol 12 (12) ◽  
pp. 7014-7022
Author(s):  
Anil Kumar Dubey ◽  
Madhubala Kasar ◽  
Ravi Prakash Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we prove a common xed point theorem for weakly compatible mappings in complex valued b-metric space and also improve the condition of contraction of the results of M. Kumar et al.[7]. Further, we prove common xed point theorems for weakly compatible mappings with (E.A.) property and (CLRg) property.

scholarly journals Weakly Compatible Maps Using E.A. and (CLR) Properties in Complex Valued G-Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Balbir Singh ◽  
Vishal Gupta ◽  
Sanjay Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Weakly Compatible ◽  
Complex Valued ◽  
Common Fixed Point Theorems

We introduce the notion of complex valued G-metric spaces and prove common fixed point theorems for weakly compatible maps along with E.A. and (CLR) properties in complex valued G-metric spaces.

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