scholarly journals Various Fixed Point Theorems in Complex Valued b-Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Anil Kumar Dubey ◽  
Manjula Tripathi ◽  
Ravi Prakash Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Control Functions ◽  
Rational Expressions ◽  
Complex Valued

We prove some common fixed point results for a pair of mappings which satisfy generalized contractive conditions with rational expressions having point-dependent control functions as coefficients in complex valued b-metric spaces. The results of this paper generalize and extend the several known results in complex valued b-metric spaces. Finally, examples are provided to verify the effectiveness and to usability of our main results.

scholarly journals Common Fixed Point Theorems Satisfying Contractive Type Conditions in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mahpeyker Öztürk
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Type ◽  
Weak Compatibility ◽  
Rational Expressions ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Satisfy Property

Some common fixed point theorems satisfying contractive conditions involving rational expressions and product for four mappings that satisfy property (E.A) along with weak compatibility of pairs are proved and further some results using (CLR)-property are obtained in complex valued metric spaces which generalize various results of ordinary metric spaces.

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 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 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 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.

scholarly journals Extended Simulation Function via Rational Expressions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 710 ◽  
Author(s):  
Rawan Alsubaie ◽  
Badr Alqahtani ◽  
Erdal Karapınar ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Upper Bound ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Simulation Function ◽  
Antecedent Conditions ◽  
Rational Expressions ◽  
Common Fixed Point Theorems ◽  
Rational Type

In this paper, we introduce some common fixed point theorems for two distinct self-mappings in the setting of metric spaces by using the notion of a simulation function introduced in 2015. The contractivity conditions have not to be verified for all pairs of points of the space because it is endowed with an antecedent conditions. They are also of rational type because the involved terms in the contractivity upper bound are expressed, in some cases, as quotients.

Sign in / Sign up

Export Citation Format

Share Document