scholarly journals Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
A. Asif ◽  
M. Alansari ◽  
N. Hussain ◽  
M. Arshad ◽  
A. Ali
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Cauchy Sequence ◽  
Metric Spaces ◽  
Closed Ball ◽  
The Third ◽  
Important Approach ◽  
Mann’S Iteration

This manuscript investigates fixed point of single-valued Hardy-Roger’s type F -contraction globally as well as locally in a convex b -metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F -contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b -metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations.

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

scholarly journals Multivalued Fixed Point Results in Dislocated b-Metric Spaces with Application to the System of Nonlinear Integral Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 40 ◽  
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Nawab Hussain ◽  
Badriah A. S. Alamri ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Common Solution

The purpose of this paper is to find out fixed point results for a pair of semi α * -dominated multivalued mappings fulfilling a generalized locally F-dominated multivalued contractive condition on a closed ball in complete dislocated b-metric space. Some new fixed point results with graphic contractions on closed ball for a pair of multi graph dominated mappings on dislocated b-metric space have been established. An application to the existence of unique common solution of a system of integral equations is presented. 2010 Mathematics Subject Classification: 46Txx, 47H04, 47H10; 54H25.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

scholarly journals Extended partial b-metric spaces and some fixed point results

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2837-2850 ◽  
Author(s):  
V. Parvaneh ◽  
Z. Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Volterra Type ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Type Integral ◽  
Convergence Of Sequences ◽  
Weakly Contractive

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

scholarly journals Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2009
Author(s):  
Badshah-e-Rome ◽  
Muhammad Sarwar ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Of Solutions

In this article, the concept of extended fuzzy rectangular b-metric space (EFRbMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFRbMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed.

scholarly journals Coincidence and common fixed point theorems for four mappings satisfying (αs, F)-contraction

2018 ◽  
Vol 23 (5) ◽  
pp. 664-690 ◽  
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Common Solution ◽  
Type Integral ◽  
Common Fixed Point Theorems

In this paper, we manifest some coincidence and common fixed point theorems for four self-mappings satisfying Círíc-type and Hardy–Rogers-type (αs,F)-contractions defined on an αs-complete b-metric space. We apply these results to infer several new and old corresponding results in ordered b-metric spaces and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We present examples to validate our results. We discuss an application of main result to show the existence of common solution of the system of Volterra type integral equations.

Coincidence of multivalued mappings on metric spaces with a graph

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4543-4554
Author(s):  
Muhammad Khana ◽  
Akbar Azam ◽  
Ljubisa Kocinac
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Space ◽  
Fractional Integral ◽  
Homotopy Theory ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Coincidence Points ◽  
Urysohn Integral Equations

In this article the coincidence points of a self mapping and a sequence of multivalued mappings are found using the graphic F-contraction. This generalizes Mizoguchi-Takahashi?s fixed point theorem for multivalued mappings on a metric space endowed with a graph. As applications we obtain a theorem in homotopy theory, an existence theorem for the solution of a system of Urysohn integral equations, and for the solution of a special type of fractional integral equations.

scholarly journals Existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 128-145 ◽  
Author(s):  
Oratai Yamaod ◽  
Wutiphol Sintunavarat ◽  
Yeol Je Cho
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Common Solution ◽  
Fixed Point Methods ◽  
Common Fixed Point Theorems

AbstractIn this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.

scholarly journals Contractive Mapping in Generalized, Ordered Metric Spaces with Application in Integral Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
L. Gholizadeh ◽  
R. Saadati ◽  
W. Shatanawi ◽  
S. M. Vaezpour
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Ordered Metric Space ◽  
Partially Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Partially Ordered

We consider the concept of -distance on a complete, partially ordered -metric space and prove some fixed point theorems. Then, we present some applications in integral equations of our obtained results.

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