On the Hyers-Ulam-Rassias Stability of Mappings

1998 ◽  
pp. 465-469 ◽  
Author(s):  
P. Găvruţă
Keyword(s):  
Stability Of Mappings ◽  
Rassias Stability

scholarly journals STABILITY OF MAPPINGS ON MULTI-NORMED SPACES

2007 ◽  
Vol 49 (2) ◽  
pp. 321-332 ◽  
Author(s):  
H. G. DALES ◽  
MOHAMMAD SAL MOSLEHIAN
Keyword(s):  
Stability Theorem ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Additive Equation ◽  
Stability Of Mappings ◽  
Rassias Stability

AbstractIn this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers–Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

scholarly journals Hyers-Ulam-Rassias stability of (m, n)-Jordan derivations

2020 ◽  
Vol 18 (1) ◽  
pp. 1615-1624
Author(s):  
Guangyu An ◽  
Ying Yao
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Rassias Stability

Abstract In this paper, we study the Hyers-Ulam-Rassias stability of ( m , n ) (m,n) -Jordan derivations. As applications, we characterize ( m , n ) (m,n) -Jordan derivations on C ⁎ {C}^{\ast } -algebras and some non-self-adjoint operator algebras.

scholarly journals Local stability of mappings on multi-normed spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
Batool Noori ◽  
M. B. Moghimi ◽  
Abbas Najati ◽  
J. M. Rassias
Keyword(s):  
Local Stability ◽  
Normed Spaces ◽  
Stability Of Mappings

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 Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

scholarly journals Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nguyen Ngoc Phung ◽  
Bao Quoc Ta ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Successive Approximation ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Point Method ◽  
Successive Approximation Method ◽  
Rassias Stability

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

scholarly journals Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Janfada ◽  
R. Shourvazi
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
General Solutions ◽  
Rassias Stability

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation , , on non-Archimedean normed spaces.

scholarly journals Non-Archimedean Hyers-Ulam-Rassias stability of m-variable functional equation

2012 ◽  
Vol 2012 (1) ◽  
pp. 111 ◽  
Author(s):  
H Azadi Kenary ◽  
H Rezaei ◽  
M Sharifzadeh ◽  
DY Shin ◽  
JR Lee
Keyword(s):  
Functional Equation ◽  
Rassias Stability

Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

2021 ◽  
pp. 2150059
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Positive Solution ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Fuzzy Variable ◽  
Point Theory ◽  
Equation Model ◽  
Theory Approach ◽  
Fractional Differential ◽  
Novel Coronavirus ◽  
Rassias Stability

This work provides a new fuzzy variable fractional COVID-19 model and uses a variable fractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivatives in the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existence and uniqueness conditions. We choose an appropriate mapping and with the help of the upper/lower solutions method. We prove the existence of a positive solution for the proposed fuzzy variable fractional COVID-19 model and also obtain the result on the existence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate the results on maximum and minimum solutions for the fuzzy variable fractional COVID-19 model.

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