scholarly journals Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces – Revisited

2017 ◽  
Vol 31 (1) ◽  
pp. 173-185
Author(s):  
Mian Bahadur Zada ◽  
Muhammad Sarwar
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Type ◽  
Made In

Abstract In our previous work titled “Fixed Point Results Satisfying Rational type Contractive Conditions in Complex Valued Metric Spaces”[Ann. Math. Sil. 30 (2016), 89-110], some errors has been made in the main results (Theorem 3.1, Theorem 3.7 and Theorem 3.22), that may misguide the readers. This note provides corrections of these errors.

scholarly journals Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

2016 ◽  
Vol 30 (1) ◽  
pp. 89-110
Author(s):  
Poom Kumam ◽  
Muhammad Sarwar ◽  
Mian Bahadur Zada
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Type

AbstractThe aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.

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 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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