scholarly journals Solvability and algorithms of generalized nonlinear variational-like inequalities in reflexive Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Haiyan Gao ◽  
Lili Wang ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Minimax Inequality ◽  
Reflexive Banach Spaces ◽  
Uniqueness Of Solutions ◽  
Auxiliary Principle Technique

Abstract This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also an auxiliary variational-like inequality and, by utilizing the minimax inequality, get the existence and uniqueness of solutions for the auxiliary variational-like inequality, which is used to suggest an iterative algorithm for solving the generalized nonlinear variational-like inequality. Under certain conditions, by means of the auxiliary principle technique, we both establish the existence and uniqueness of solutions for the generalized nonlinear variational-like inequality and discuss the convergence of iterative sequences generated by the iterative algorithm. Our results extend, improve, and unify several known results in the literature.

scholarly journals RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Linear Maps ◽  
Retracted Article

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

scholarly journals Fixed-Point Iterative Algorithm for the Linear Fredholm-Volterra Integro-Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. J. López Linares
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Point Theorem ◽  
Numerical Algorithm ◽  
Linear Case ◽  
Integro Differential Equation ◽  
Equivalent Version

With the aid of fixed-point theorem (an equivalent version for the linear case) and biorthogonal systems in adequate Banach spaces, the problem of approximating the solution of a linear Fredholm-Volterra integro-differential equation is turned into a numerical algorithm, so that it can be solved numerically.

Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Ahmadi ◽  
Rahmatollah Lashkaripour ◽  
Hamid Baghani ◽  
Shapour Heidarkhani
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Krasnoselskii’S Fixed Point Theorem

AbstractIn this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any ${n}_{1},{n}_{2}\in \mathrm{ℕ}$. We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.

scholarly journals On Existence and uniqueness to solutions nonlocal integrodifferential equations

2018 ◽  
Vol 1 (25) ◽  
pp. 493-508
Author(s):  
Fawzi Mutter Ismaael
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem

The Study aims in this paper to give and investigate the existence and uniqueness of mild solutions to nonlinear functional integrodifferential equations in Banach Spaces. the fixed point theorem, according to Sadovskii and sutible necessary conditions, are concepts consulted to obtain the results in the work

scholarly journals New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra–Fredholm Integro-Dynamic Equations

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 19
Author(s):  
Kalpana Gopalan ◽  
Sumaiya Tasneem Zubair ◽  
Thabet Abdeljawad ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Dynamic Equation ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Research Article ◽  
Type Spaces

The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an initial value problem associated with a nonlinear Volterra–Fredholm integro-dynamic equation and examine the existence and uniqueness of solutions via fixed point theorem in the setting of complete triple controlled metric type spaces. Furthermore, the theorem is applied to illustrate the existence of a unique solution to an integro-dynamic equation.

scholarly journals On a fixed point theorem and its application in dynamic programming

2015 ◽  
Vol 9 (2) ◽  
pp. 221-244 ◽  
Author(s):  
Ángel Almeida ◽  
Antonio-Francisco Roldán-López-de-Hierro ◽  
Kishin Sadarangani
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Uniqueness Of Solutions ◽  
Rational Type

In this paper, we present some fixed point theorems for contractions of rational type. These theorems generalize some other results appearing in the literature. Moreover, we present some examples illustrating our results. Finally, we present an application to the study of the existence and uniqueness of solutions to a class of functional equations arising in dynamic programming.

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