On new stability results for generalized Cauchy functional equations on groups by using Brzdȩk’s fixed point theorem

2015 ◽  
Vol 18 (1) ◽  
pp. 45-59 ◽  
Author(s):  
Laddawan Aiemsomboon ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Functional Equations On Groups ◽  
Stability Results

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2020 ◽  
Vol 102 (2) ◽  
pp. 293-302
Author(s):  
THEERAYOOT PHOCHAI ◽  
SATIT SAEJUNG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Equations ◽  
General Linear ◽  
Several Variables ◽  
Linear Functional Equations

Zhang [‘On hyperstability of generalised linear functional equations in several variables’, Bull. Aust. Math. Soc.92 (2015), 259–267] proved a hyperstability result for generalised linear functional equations in several variables by using Brzdęk’s fixed point theorem. We complete and extend Zhang’s result. We illustrate our results for general linear equations in two variables and Fréchet equations.

Ulam-Hyers stability theorem by tripled fixed point theorem

2016 ◽  
Vol 56 (1) ◽  
pp. 77-97
Author(s):  
Animesh Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Stability Theorem ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Vector Valued ◽  
Stability Results

AbstractThis paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

scholarly journals Asymptotic Stability Results for Nonlinear Fractional Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Fulai Chen ◽  
Zhigang Liu
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Stability Of Solutions ◽  
Fractional Difference ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Difference Equations ◽  
Stability Results

We present some results for the asymptotic stability of solutions for nonlinear fractional difference equations involvingRiemann-Liouville-likedifference operator. The results are obtained by using Krasnoselskii's fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results.

scholarly journals Existence, uniqueness, approximation of solutions and Ealpha-Ulam stability results for a class of nonlinear fractional differential equations involving psi-Caputo derivative with initial conditions

2021 ◽  
Vol 25 (1) ◽  
pp. 1-30
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
Gaston N'guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Ulam Stability ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Stability Results

The main purpose of this paper is to study the existence, uniqueness, Ea-Ulam stability results, and other properties of solutions for certain classes of nonlinear fractional differential equations involving the ps-Caputo derivative with initial conditions. Modern tools of functional analysis are applied to obtain the main results. More precisely using Weissinger's fixed point theorem and Schaefer's fixed point theorem the existence and uniqueness results of solutions are proven in the bounded domain. While the well known Banach fixed point theorem coupled with Bielecki type norm are used with the end goal to establish sufficient conditions for existence and uniqueness results on unbounded domains. Meanwhile, the monotone iterative technique combined with the method of upper and lower solutions is used to prove the existence and uniqueness of extremal solutions. Furthermore, by means of new generalizations of Gronwall's inequality, different kinds of Ea-Ulam stability of the proposed problem are studied. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility and correctness of the main results.

scholarly journals Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ -Caputo Derivative in Banach and Fréchet Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
G. N’Guérékata
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Ulam Stability ◽  
Fréchet Spaces ◽  
Existence Of A Solution ◽  
Gronwall’S Inequality ◽  
Condensing Operators ◽  
Stability Results

Our aim in this paper is to investigate the existence, uniqueness, and Mittag–Leffler–Ulam stability results for a Cauchy problem involving ψ -Caputo fractional derivative with positive constant coefficient in Banach and Fréchet Spaces. The techniques used are a variety of tools for functional analysis. More specifically, we apply Weissinger’s fixed point theorem and Banach contraction principle with respect to the Chebyshev and Bielecki norms to obtain the uniqueness of solution on bounded and unbounded domains in a Banach space. However, a new fixed point theorem with respect to Meir–Keeler condensing operators combined with the technique of Hausdorff measure of noncompactness is used to investigate the existence of a solution in Banach spaces. After that, by means of new generalizations of Grönwall’s inequality, the Mittag–Leffler–Ulam stability of the proposed problem is studied on a compact interval. Meanwhile, an extension of the well-known Darbo’s fixed point theorem in Fréchet spaces associated with the concept of measures of noncompactness is applied to obtain the existence results for the problem at hand. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems.

Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations

2014 ◽  
Vol 52 (1) ◽  
Author(s):  
Hemant Kumar Nashine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Functional Equations ◽  
Uniqueness Of Solutions ◽  
System Of Functional Equations ◽  
Altering Distance ◽  
Common Limit ◽  
Common Limit Range Property

AbstractThe aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.

Sign in / Sign up

Export Citation Format

Share Document