Fuzzy Fixed Point Results Via Rational Type Contractions Involving Control Functions in Complex-Valued Metric Spaces

2018 ◽  
Vol 12 (4) ◽  
pp. 861-875 ◽  
Author(s):  
Humaira Humaira ◽  
Muhammad Sarwar ◽  
Cemil Tunc
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Control Functions ◽  
Fuzzy Fixed Point ◽  
Complex Valued ◽  
Rational Type

scholarly journals Fuzzy Fixed Point Results For Φ Contractive Mapping with Applications

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Humaira ◽  
Muhammad Sarwar ◽  
G. N. V. Kishore
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contractive Mapping ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Control Functions ◽  
Complex Valued Metric Space ◽  
Fuzzy Fixed Point ◽  
Complex Valued ◽  
Rational Type

In this paper, using rational type contractions, common fuzzy fixed point result for Φ contractive mappings involving control functions as coefficients of contractions in the setting of complex-valued metric space is established. The derived results generalizes some result in the existing literature. To show the validity of the derived results an appropriate example and applications are also discussed.

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 Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saif Ur Rehman ◽  
Ronnason Chinram ◽  
Chawalit Boonpok
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Type Equation ◽  
Integral Type ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Type ◽  
Fuzzy Fixed Point ◽  
Existing Result ◽  
Rational Type

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under the rational type fuzzy-contraction conditions in fuzzy metric spaces with illustrative examples to support our results. This new concept will play a very important role in the theory of fuzzy fixed point results and can be generalized for different contractive type mappings in the context of fuzzy metric spaces. Moreover, we present an application of a nonlinear integral type equation to get the existing result for a unique solution to support our work.

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 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 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 .

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