scholarly journals On a Fixed Point Theorem with Application to Integral Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Of Solution

We introduce the notion of dualistic Geraghty’s type contractions. We prove some fixed point theorems for ordered mappings satisfying the abovementioned contractions. We discuss an application of our fixed point results to show the existence of solution of integral equations.

scholarly journals Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
N. Hussain ◽  
I. Iqbal ◽  
Badriah A. S. Alamri ◽  
M. A. Kutbi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Nadler’S Fixed Point Theorem ◽  
Proper Generalization

In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.

scholarly journals Fixed-Point Theorem for Nonlinear F -Contraction via w -Distance

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Uniqueness Of A Solution

The aim of this paper is to introduce a notion of ϕ , F -contraction defined on a metric space with w -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.

Random fixed point theorem in generalized Banach space and applications

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Moulay Larbi Sinacer ◽  
Juan Jose Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Random Operator ◽  
Existence Of Solution ◽  
Random Fixed Point ◽  
Random Differential Equations ◽  
Random Fixed Point Theorem

AbstractIn this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.

Fixed point results for nonlinear contractions with application to integral equations

2019 ◽  
Vol 12 (07) ◽  
pp. 2050007
Author(s):  
Rahul Shukla ◽  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Integral Equations ◽  
Common Fixed Point Theorems ◽  
Nonlinear Contractions

We present a number of fixed and common fixed point theorems for a class of nonlinear contractions in metric spaces and metric spaces endowed with graphs. Our results complement, extend and generalize a number of fixed point theorems including a recent fixed point theorem of Kim et al. [Suzuki-type of common fixed theorem in metric spaces, J. Nonlinear Convex Anal. 16 (2015) 1779–1786]. We also discuss an application to a system of integral equations.

scholarly journals On solvability of infinite system of integral equations of Volterra together with Hammerstein type in the Fréchet spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2055-2069
Author(s):  
Shahram Banaei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Of Solutions ◽  
Fréchet Spaces ◽  
System Of Integral Equations

In this paper, we prove some fixed point theorems associated with Tychonoff fixed point theorem and measure of noncompactness in the Fr?chet spaces. Moreover, as an application of our results, we analyze the existence of solutions for infinite system of integral equations of Volterra together with Hammerstein type. Finally, we present an example to illustrate the effectiveness of our results.

scholarly journals New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1090 ◽  
Author(s):  
Pradip Debnath ◽  
Hari Mohan Srivastava
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Multivalued Maps ◽  
Proper Extension ◽  
Metric Function ◽  
Symmetric Property

The metric function generalizes the concept of distance between two points and hence includes the symmetric property. The aim of this article is to introduce a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. We show that our result is applicable to a class of mappings where neither the multivalued version of Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points. Application of our result to the solution of integral equations has been provided. A multivalued Reich type generalized version of the result is also established.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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