scholarly journals Approximate Homomorphisms and Derivations on Normed Lie Triple Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hark-Mahn Kim ◽  
Juri Lee
Keyword(s):  
Ulam Stability ◽  
Real Numbers ◽  
Triple Systems ◽  
Additive Equation ◽  
Stability Results

We investigate the generalized Hyers-Ulam stability of homomorphisms and derivations on normed Lie triple systems for the following generalized Cauchy-Jensen additive equationr0f((s∑j=1pxj+t∑j=1dyj)/r0)=s∑j=1p‍f(xj)+t∑j=1d‍f(yj), wherer0,s, and  tare nonzero real numbers. As a results, we generalize some stability results concerning this 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 Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Saïd Abbas ◽  
Eman Alaidarous ◽  
Mouffak Benchohra ◽  
Juan J. Nieto
Keyword(s):  
Integral Equations ◽  
Fractional Integral ◽  
Existence Result ◽  
Existence Results ◽  
Stieltjes Integral ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Stability Results ◽  
Rassias Stability

We give some existence results and Ulam stability results for a class of Hadamard-Stieltjes integral equations. We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability.

scholarly journals On the Stability of -Derivations and Lie -Algebra Homomorphisms on Lie -Algebras: A Fixed Points Method

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Points ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
The Stability ◽  
Algebra Homomorphisms ◽  
Stability Results

We investigate new generalized Hyers-Ulam stability results for -derivations and Lie -algebra homomorphisms on Lie -algebras associated with the additive functional equation:

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 and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

2021 ◽  
Author(s):  
ABDELLOUAHAB Naimi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Stability Study ◽  
Ulam Stability ◽  
Differential Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

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