scholarly journals On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
O. Baghani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Operator

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.

scholarly journals On the existence and uniqueness of the solution of a nonlinear integral equation

2019 ◽  
Vol 488 (6) ◽  
pp. 595-598
Author(s):  
M. V. Nikolaev ◽  
A. A. Nikitin
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Spatial Model ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Sufficient Conditions ◽  
Biological Communities ◽  
Uniqueness Of The Solution

In this paper we study the nonlinear integral equation that arose in the spatial model of biological communities developed by Austrian scientists Ulf Dieckmann and Richard Law. Sufficient conditions for the existence of the solution of this equation (the fixed point of the integral operator) were found. The question of uniqueness of the solution is also studied.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1253-1264 ◽  
Author(s):  
Hüseyin Işik ◽  
Duran Türkoğlu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Nonlinear Problems ◽  
Monotone Mappings ◽  
Mixed Monotone Property

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

scholarly journals Recent Fixed-Point Results for θ − Contraction Mappings in Rectangular M − Metric Spaces with Supportive Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mustafa Mudhesh ◽  
Hasanen A. Hammad ◽  
Habes Alsamir ◽  
Muhammad Arshad ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Theoretical Result ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Uniqueness Of The Solution

The goal of this manuscript is to present a new fixed-point theorem on θ − contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with θ − contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

scholarly journals A Nonlinear Integral Equation Related to Infectious Diseases

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Integral Equation ◽  
Infectious Diseases ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Numerical Algorithms ◽  
Data Dependence ◽  
Uniqueness Of Solutions

In this paper, a nonlinear integral equation related to infectious diseases is investigated. Namely, we first study the existence and uniqueness of solutions and provide numerical algorithms that converge to the unique solution. Next, we study the lower and upper subsolutions, as well as the data dependence of the solution.

scholarly journals Solving an Integral Equation by Using Fixed Point Approach in Fuzzy Bipolar Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam ◽  
Absar Ul Haq ◽  
Fahd Jarad ◽  
Imran Abbas Baloch
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Fixed Point Approach ◽  
Uniqueness Of The Solution ◽  
Theoretical Results

The purpose of this manuscript is to obtain some fixed point results under mild contractive conditions in fuzzy bipolar metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation was studied as a kind of applications.

scholarly journals Fixed point of sum for concave and convex operators with applications

1988 ◽  
Vol 37 (1) ◽  
pp. 81-87
Author(s):  
Li Bingyou
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Theorems ◽  
Linear Spaces ◽  
Existence And Uniqueness Theorems ◽  
Ordered Linear Spaces ◽  
Convex Operators

In this paper we study fixed points of sums of α-concave and (−α)-convex operators in γ-complete partially ordered linear spaces. As an application we obtain existence and uniqueness theorems for solutions of a certain type of nonlinear integral equation.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

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