scholarly journals Rational Type Compatible Single-Valued Mappings via Unique Common Fixed Point Findings in Complex-Valued b-Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Shahid Mehmood ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Mabrook Al-Rakhami ◽  
Abdu Gumaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Integral Type ◽  
Common Solution ◽  
Main Work ◽  
Complex Valued ◽  
Rational Type ◽  
Unique Common Fixed Point

In this paper, we establish some new generalized rational type common fixed point results for compatible three self-mappings in complex-valued b-metric space, in which a one self-map is continuous. In support of our results, we present some illustrative examples to verify the validity of our main work. Moreover, we present the application of two Urysohn integral type equations (UITEs) for the existence of a common solution to support our work. The UITEs are v 1 p = ∫ k 1 k 2 Q 1 p , r , v 1 r d r + ℏ 1 p and v 2 p = ∫ k 1 k 2 Q 2 p , r , v 2 r d r + ℏ 2 p , where p ∈ k 1 , k 2 , v 1 , v 2 , ℏ 1 , ℏ 2 ∈ V , where V = C k 1 , k 2 , ℝ n is the set of all real-valued continuous functions defined on k 1 , k 2 and Q 1 , Q 2 : k 1 , k 2 × k 1 , k 2 × ℝ n ⟶ ℝ n .

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 two families of multivalued A–dominated contractive mappings on closed ball with applications

2019 ◽  
Vol 17 (1) ◽  
pp. 1350-1360 ◽  
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
Nonlinear Integral Equations ◽  
Common Solution ◽  
Contractive Mappings ◽  
Rational Type

Abstract The purpose of this paper is to find common fixed point results for two families of multivalued mappings fulfilling generalized rational type A–dominated contractive conditions on a closed ball in complete dislocated b-metric spaces. Some new fixed point results with graphic contractions on a closed ball for two families of multi-graph dominated mappings on dislocated b-metric space have been established. An application to the unique common solution of two families of nonlinear integral equations is presented to show the novelty of our results.

scholarly journals Unique Common Fixed Point Results with Application in Fuzzy Metric Spaces

2019 ◽  
Vol 9 (2) ◽  
pp. 2527-2529
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Fuzzy Theory ◽  
Integral Type ◽  
Generalized Contraction ◽  
Communication And Technology ◽  
Common Fixed Point Theorem ◽  
Type Contraction ◽  
Unique Common Fixed Point

Fixed points in fuzzy theory plays a very significant task in the field of mathematical and computer sciences. This theory has numerous applications in the area of communication and technology, computer science and information security and many others. Many researchers established the results of point for an assortment of mappings in different metric spaces. In present paper, our aim is to establish a common fixed point theorem satisfying generalized contraction in FMS. We also bestow an application for integral type contraction

scholarly journals Generalized Common Fixed Point Results with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Marwan Amin Kutbi ◽  
Muhammad Arshad ◽  
Jamshaid Ahmad ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Common Solution ◽  
Urysohn Integral Equations ◽  
The Common ◽  
Complex Valued

We obtained some generalized common fixed point results in the context of complex valued metric spaces. Moreover, we proved an existence theorem for the common solution for two Urysohn integral equations. Examples are presented to support our results.

scholarly journals Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Sumit Chandok ◽  
Deepak Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Weakly Compatible ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.

scholarly journals Common Fixed Point Theorems of Compatible Maps in Complex Valued b-Metric Spaces

2020 ◽  
Vol 12 (4) ◽  
pp. 431-446
Author(s):  
G. Yadav ◽  
R. K. Sharma ◽  
G. L. Prajapati
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Weak Compatibility ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Rational Type

In a paper Mukheimer established some results regarding common fixed point of two self mappings in a complex valued b-metric space satisfying a rational type contractive condition. In this paper we have established a common fixed point theorem by making use of compatibility and weak compatibility of self mappings satisfying generalized rational inequality of four mappings as opposed to two self mappings in a complex valued b – metric space. Some concrete examples have also been presented to verify the effectiveness and applicability of established results. Towards the end, an application to solution of Urysohn’s integral equations has also been presented to substantiate the usability of the obtained results. Results of this paper generalize the results of Mukheimer and some other earlier results. Theorems approved in this article will be supportable for researchers to work on rational contractions with more than two pair of self mappings.  

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