scholarly journals Fixed point results for hybrid contractions in Menger metric spaces with application to integral equations

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2151-2164
Author(s):  
Ayub Samadi ◽  
Nawab Hussain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence Result ◽  
Metric Spaces ◽  
Multivalued Mappings

Here the notion of ?-H?-contraction has been proposed to construct some fixed point results of single-valued and multivalued mappings in Menger PM spaces. In addition, an existence result to an integral equation is concerned to justify the obtained results.

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 Solving a Class of Integral Equations via Contractive Mapping with Rational Type

2020 ◽  
Vol 13 (4) ◽  
pp. 995-1015
Author(s):  
Abdullah Abdullah ◽  
Muhammad Sarwar ◽  
Zead Mustafa ◽  
Mohammed M.M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Contractive Mapping ◽  
Coupled Fixed Point Theorem ◽  
Set Up ◽  
Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

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 The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

scholarly journals Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

scholarly journals Solving an Integral Equation via Fuzzy Triple Controlled Bipolar Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3181
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Zoran D. Mitrović ◽  
Monica-Felicia Bota
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Recent Result ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces

In this paper, motivated by the recent result of Sezen, we introduce the notion of fuzzy triple controlled bipolar metric space and prove some fixed point results in this framework. Our results generalize and extend some of the well-known results from the literature. We also explore some of the applications of our key results to integral equations.

scholarly journals A random version of Schaefer's fixed point theorem with applications to functional random integral equations

2004 ◽  
Vol 35 (3) ◽  
pp. 197-206 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Nonlinear Functional ◽  
Carathéodory Conditions ◽  
Random Integral

In this paper a random version of a fixed-point theorem of Schaefer is obtained and it is further applied to a certain nonlinear functional random integral equation for proving the existence result under Caratheodory conditions.

scholarly journals Modified F-contractions via α-admissible mappings and application to integral equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1141-1148 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapinar ◽  
Habib Yazidi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Spaces

In this paper, we introduce the concept of a modified F-contraction via ?-admissible mappings and propose some theorems that guarantee the existence and uniqueness of fixed point for such mappings in the frame of complete metric spaces. We also provide some illustrative examples. Moreover, we consider an application solving an integral equation.

scholarly journals Feng–Liu-type fixed point result in orbital b-metric spaces and application to fractal integral equation

2021 ◽  
Vol 26 (3) ◽  
pp. 522-533
Author(s):  
Hemant Kumar Nashine ◽  
Lakshmi Kanta Dey ◽  
Rabha W. Ibrahim ◽  
Stojan Radenovi´c
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Lower Semicontinuous ◽  
Lower Semicontinuous Functions ◽  
Fixed Point Result ◽  
Semicontinuous Functions

In this manuscript, we establish two Wardowski–Feng–Liu-type fixed point theorems for orbitally lower semicontinuous functions defined in orbitally complete b-metric spaces. The obtained results generalize and improve several existing theorems in the literature. Moreover, the findings are justified by suitable nontrivial examples. Further, we also discuss ordered version of the obtained results. Finally, an application is presented by using the concept of fractal involving a certain kind of fractal integral equations. An illustrative example is presented to substantiate the applicability of the obtained result in reducing the energy of an antenna.

scholarly journals Fixed Points forψ-Graphic Contractions with Application to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Hussain ◽  
S. Al-Mezel ◽  
P. Salimi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces

The aim of this paper is to define modified weakα-ψ-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangularα-admissibility. As an application, we prove new fixed point results for graphic weakψ-contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.

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