scholarly journals Common Fixed Point Theorems for Weakly Contractions in Rectangular b -Metric Spaces with Supportive Applications

2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Hongyan Guan ◽  
Jianju Li ◽  
Yan Hao
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Common Fixed Point Theorems

In this manuscript, two new classes of generalized weakly contractions are introduced and common fixed point results concerning the new contractions are proved in the context of rectangular b -metric spaces. Also, some examples are included to present the validity of our theorems. As an application, we provide the existence and uniqueness of solution of an integral equation.

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 Complex Valued b-Metric Spaces and Common Fixed Point Theorems under Rational Contractions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Anil Kumar Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued b-metric space. The obtained results generalize and extend some of the well-known results in the literature.

scholarly journals Some fuzzy common fixed point theorems using common limit in the range property with an application

2020 ◽  
Vol 24 (2) ◽  
pp. 33-49
Author(s):  
Ved Bhardwaj ◽  
Kamal Wadhwa
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Common Limit ◽  
Uniqueness Of The Solution ◽  
Common Fixed Point Theorems

In the present paper, we prove some common fixed point theorems for mappings satisfying common limit in the range property in M-fuzzy metric space. Further, we prove fixed point theorem for ph-contractive conditions in aforesaid spaces with the illustration of an example. As an application of our result, we study the existence and uniqueness of the solution of integral equation (Volterra integral equations of the second kind) with instances.

scholarly journals Common fixed point theorems under an implicit contractive condition on metric spaces endowed with an arbitrary binary relation and an application

2019 ◽  
pp. 2050146
Author(s):  
Md Ahmadullah ◽  
Mohammad Imdad ◽  
Mohammad Arif
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Binary Relation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Common Fixed Point Theorems

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well-known contraction conditions in one go besides yielding several new ones. We also provide an example to demonstrate the generality of our results over several well-known corresponding results of the existing literature. Finally, we utilize our results to prove an existence theorem for ensuring the solution of an integral equation.

scholarly journals Some Common Fixed Point Theorems in Complex Valuedb-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Aiman A. Mukheimer
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Result ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valuedb-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valuedb-metric spaces. Some examples are given to illustrate the main results.

scholarly journals Common Fixed Point Results for Generalized g − α s p , ψ , φ Contractive Mappings with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jianju Li ◽  
Hongyan Guan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
New Class ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

In this paper, we introduce a new class of g − α s p − admissible mappings and prove some common fixed point theorems involving this new class of mappings which satisfy generalized contractive conditions in the framework of b − metric spaces. We also provide two examples to show the applicability and validity of our results. Meanwhile, we present an application to the existence of solutions to an integral equation by means of one of our results.

scholarly journals Some fixed point theorems of rational type contraction in b-metric spaces

2021 ◽  
Vol 7 (3) ◽  
pp. 350-363
Author(s):  
Merdaci Seddik ◽  
Hamaizia Taieb
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Type Mapping ◽  
Contractive Type ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction

Abstract In this paper, we prove some common fixed point theorems satisfying contractive type mapping in the setting of b-metric spaces. The presented theorem is an extension the results of M. Sarwar and M. U. Rahman [23] as well as a generalization of many well-known results in the literature through the context of b-metric spaces. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

scholarly journals Common Fixed Point Theorems for Contractive Mappings of Integral Type in G -Metric Spaces and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Fengrong Zhang ◽  
Xiangshuai Zhang ◽  
Yan Hao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Contractive Mappings ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

Two common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type in G -metric spaces are demonstrated. The results obtained in this paper generalize and differ from a few results in the literature and are used to prove the existence and uniqueness of common bounded and continuous solutions for certain functional equations and nonlinear Volterra integral equations. A nontrivial example is included.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

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