scholarly journals Fixed point results for a pair of fuzzy mappings and related applications in b-metric like spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tahair Rasham ◽  
Giuseppe Marino ◽  
Aqeel Shahzad ◽  
Choonkill Park ◽  
Abdullah Shoaib
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Unique Solution ◽  
Integral Equations ◽  
Bounded Solution ◽  
System Of Integral Equations

AbstractThis paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming.

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 Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Atiya Perveen ◽  
Idrees A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Spaces ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

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 Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Doaa Filali ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Banach Algebras ◽  
System Of Integral Equations ◽  
Different Types ◽  
Common Fixed Point Theorems

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

scholarly journals Fixed points of hesitant fuzzy set-valued maps with applications

2021 ◽  
Vol 13 (3) ◽  
pp. 711-726
Author(s):  
M.S. Shagari ◽  
A. Azam
Keyword(s):  
Functional Equation ◽  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Fuzzy Set ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Hesitant Fuzzy Set ◽  
Alpha Beta

In this paper, the notion of hesitant fuzzy fixed points is introduced. To this end, we define Suzuki-type $(\alpha,\beta)$-weak contractions in the framework of hesitant fuzzy set-valued maps, thereby establishing some corresponding fixed point theorems. The presented concept herein is an extension of fuzzy set-valued and multi-valued mappings in the corresponding literature. Examples are provided to support the assertions and generality of our obtained ideas. Moreover, one of our results is applied to investigate sufficient conditions for existence of a class of functional equation arising in dynamic programming.

scholarly journals FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

2021 ◽  
pp. 237
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Urysohn Integral Equations ◽  
Complex Valued

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature.

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 Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

2019 ◽  
Vol 9 (1) ◽  
pp. 1187-1204
Author(s):  
Agnieszka Chlebowicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Function Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Half Axis ◽  
Suitable Measure

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

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