scholarly journals Some fixed point theorems for Meir-Keeler condensing operators with applications to integral equations

2015 ◽  
Vol 22 (4) ◽  
pp. 529-541 ◽  
Author(s):  
A. Alotaibi ◽  
M. Mursaleen ◽  
S.A. Mohiuddine
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Condensing Operators

scholarly journals Meir-Keeler condensing operators and applications

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2175-2188
Author(s):  
Amor Hadj ◽  
Abdelhak Traiki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Weak Noncompactness ◽  
Arbitrary Measure ◽  
Condensing Operator ◽  
Condensing Operators ◽  
Open Question ◽  
Nonlinear Hybrid

Motivated by the open question posed by H. K. XU in [39] (Question 2:8), Belhadj, Ben Amar and Boumaiza introduced in [5] the concept of Meir-Keeler condensing operator for self-mappings in a Banach space via an arbitrary measure of weak noncompactness. In this paper, we introduce the concept of Meir- Keeler condensing operator for nonself-mappings in a Banach space via a measure of weak noncompactness and we establish fixed point results under the condition of Leray-Schauder type. Some basic hybrid fixed point theorems involving the sum as well as the product of two operators are also presented. These results generalize the results on the lines of Krasnoselskii and Dhage. An application is given to nonlinear hybrid linearly perturbed integral equations and an example is also presented.

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.

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

scholarly journals Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

2019 ◽  
Vol 52 (1) ◽  
pp. 166-182 ◽  
Author(s):  
Habib ur Rehman ◽  
Dhananjay Gopal ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo’S Fixed Point Theorem ◽  
Condensing Operators ◽  
Functional Integral Equations

AbstractIn this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we defineα-ψandβ-ψcondensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

scholarly journals Fixed Point Theorems for ${\mathscr{Z}}_{\vartheta}$ -Contraction and Applications to Nonlinear Integral Equations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 120023-120029
Author(s):  
Xiangling Li ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Ekrem Savas
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equations

scholarly journals A Solution for Volterra Fractional Integral Equations by Hybrid Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 694 ◽  
Author(s):  
Alqahtani ◽  
Aydi ◽  
Karapınar ◽  
Rakočević
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Linear Type ◽  
Linear And Nonlinear ◽  
Nonlinear Contractions ◽  
Type Contraction

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

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