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 Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

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 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.

Some new common fixed point theorems for contractive selfmappings with applications

2021 ◽  
pp. 2250080
Author(s):  
Youssef Touail ◽  
Driss El Moutawakil
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Topological Spaces ◽  
System Of Differential Equations ◽  
System Of Functional Equations ◽  
Common Fixed Point Theorems

In this paper, we first prove a new common fixed point in general topological spaces with a [Formula: see text]-distance. From this result, we establish two common fixed points for two new classes of contractive selfmappings in complete bounded metric spaces. Furthermore, an application to a system of differential equations and another to a system of functional equations arising in dynamic programming are given.

Some Fixed Point Theorems Under Contractive Type Conditions in Complex Valued Metric Spaces

2017 ◽  
Vol 84 (1-2) ◽  
pp. 96
Author(s):  
G. S. Saluja
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Rational Expression ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

The purpose of this paper is to establish some fixed point and common fixed point theorems under contractive type conditions involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize some previous works from the existing literature.

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