Existence and stability results for a system of operator equations via fixed point theory for nonself orbital contractions

2019 ◽  
Vol 21 (3) ◽  
Author(s):  
Adrian Petruşel ◽  
Gabriela Petruşel ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Operator Equations ◽  
Existence And Stability ◽  
System Of Operator Equations ◽  
Stability Results

scholarly journals Global existence and stability results for mild solutions of random impulsive partial integro-differential equations

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 439-455 ◽  
Author(s):  
A. Vinodkumar ◽  
P. Indhumathi
Keyword(s):  
Fixed Point ◽  
Global Existence ◽  
Differential Equations ◽  
Continuous Dependence ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Stability Results

In this paper, we discuss the global existence, uniqueness, continuous dependence and exponential stability of random impulsive partial integro-differential equations is investigated. The results are obtained by using the Leray-Schauder alternative fixed point theory and Banach Contraction Principle. Finally we give an example to illustrate our abstract results.

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

scholarly journals A novel stability analysis for the Darboux problem of partial differential equations via fixed point theory

2021 ◽  
Vol 6 (11) ◽  
pp. 12894-12901
Author(s):  
El-sayed El-hady ◽  
◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Main Tool ◽  
Point Theory ◽  
Darboux Problem ◽  
Partial Differential ◽  
Stability Results

<abstract><p>We present Ulam-Hyers-Rassias (UHR) stability results for the Darboux problem of partial differential equations (DPPDEs). We employ some fixed point theorem (FPT) as the main tool in the analysis. In this manner, our results are considered as some generalized version of several earlier outcomes.</p></abstract>

scholarly journals A Study of ψ-Hilfer Fractional Boundary Value Problem via Nonlinear Integral Conditions Describing Navier Model

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3292
Author(s):  
Songkran Pleumpreedaporn ◽  
Weerawat Sudsutad ◽  
Chatthai Thaiprayoon ◽  
Juan E. Nápoles ◽  
Jutarat Kongson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Unique Property ◽  
Fractional Boundary Value Problem ◽  
Integral Conditions ◽  
Banach’S Fixed Point Theorem ◽  
Stability Results

This paper investigates existence, uniqueness, and Ulam’s stability results for a nonlinear implicit ψ-Hilfer FBVP describing Navier model with NIBCs. By Banach’s fixed point theorem, the unique property is established. Meanwhile, existence results are proved by using the fixed point theory of Leray-Schauder’s and Krasnoselskii’s types. In addition, Ulam’s stability results are analyzed. Furthermore, several instances are provided to demonstrate the efficacy of the main results.

scholarly journals Fixed Point Theory and the Ulam Stability

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Janusz Brzdęk ◽  
Liviu Cădariu ◽  
Krzysztof Ciepliński
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Stability Of Functional Equations ◽  
Banach’S Fixed Point Theorem ◽  
The Stability ◽  
First Time ◽  
Stability Results

The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.

scholarly journals Boundary Value Problem for Caputo–Fabrizio Random Fractional Differential Equations

2020 ◽  
Vol 6 (2) ◽  
pp. 218-230
Author(s):  
Fouzia Bekada ◽  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Random Operators ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Stability Results

AbstractThis article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section.

scholarly journals Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

2021 ◽  
Vol 2 (1) ◽  
pp. 47-61
Author(s):  
Laila Hashtamand
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Fixed Point Theory ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Fractional Order Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Stability Results

This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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