scholarly journals Inclusions in a Single Variable in Ultrametric Spaces and Hyers-Ulam Stability

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Magdalena Piszczek
Keyword(s):  
Functional Equations ◽  
Ulam Stability ◽  
Single Variable ◽  
Ultrametric Spaces ◽  
Stability Results

We present some properties of set-valued inclusions in a single variable in ultrametric spaces. As a consequence, we obtain stability results for the corresponding functional equations.

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

scholarly journals Fixed Points and Generalized Hyers-Ulam Stability

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
L. Cădariu ◽  
L. Găvruţa ◽  
P. Găvruţa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Open Problem ◽  
Functional Equations ◽  
Affirmative Answer ◽  
Ulam Stability ◽  
Single Variable ◽  
Result Show

In this paper we prove a fixed-point theorem for a class of operators with suitable properties, in very general conditions. Also, we show that some recent fixed-points results in Brzdęk et al., (2011) and Brzdęk and Ciepliński (2011) can be obtained directly from our theorem. Moreover, an affirmative answer to the open problem of Brzdęk and Ciepliński (2011) is given. Several corollaries, obtained directly from our main result, show that this is a useful tool for proving properties of generalized Hyers-Ulam stability for some functional equations in a single variable.

scholarly journals Functional inequalities for generalized multi-quadratic mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Single Equation ◽  
Quadratic Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Several Variables ◽  
Quadratic Mappings ◽  
Stability Results

AbstractIn this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

scholarly journals Applications of Banach Limit in Ulam Stability

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 841
Author(s):  
Roman Badora ◽  
Janusz Brzdęk ◽  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Functional Equation ◽  
Ulam Stability ◽  
Single Variable ◽  
Cauchy Equation ◽  
Banach Limit

We show how to get new results on Ulam stability of some functional equations using the Banach limit. We do this with the examples of the linear functional equation in single variable and the Cauchy equation.

scholarly journals Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

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.

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