Results 21 to 30 of about 451,551 (359)

Fuzzy normed spaces and stability of a generalized quadratic functional equation

AIMS Mathematics, 2020
In this paper, we acquire the general solution of the generalized quadratic functional equation \[ \begin{aligned} \sum_{1 \leq a < b < c \leq m}\varphi\left(r_{a}+r_{b}+r_{c}\right)&=(m-2)\sum_{1\leq a < b\leq m}\varphi\left(r_{a}+r_{b}\right) \\ &\quad-
Choonkill Park, K. Tamilvanan, B. Noori, M. B. Moghimi, A. Najati   +4 more
semanticscholar   +1 more source

Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability

International Journal of Mathematics and Mathematical Sciences, 2023
In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3 ...
Ravinder Kumar Sharma, Sumit Chandok
doaj   +1 more source

Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint

Fractal and Fractional, 2023
This manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution x∈C[0,
Carlo Cattani, Rajarama Mohan, S. Chakraverty, A. M. El-Sayed, Antisar A. A. Alhamali, E. Hamdallah, Hanaa R. Ebead   +6 more
semanticscholar   +1 more source

A New Approach to Hyers-Ulam Stability of r-Variable Quadratic Functional Equations

Journal of Function Spaces, 2021
In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑1 ...
Vediyappan Govindan, Porpattama Hammachukiattikul, Grienggrai Rajchakit, Nallappan Gunasekaran, R. Vadivel   +4 more
doaj   +1 more source

Stability of an n-variable mixed type functional equation in probabilistic modular spaces

AIMS Mathematics, 2020
In this research paper, we solve a new n-variable mixed type additive-quadratic functional equation and prove the Ulam stability of the new n-variable mixed type additive-quadratic functional equation in probabilistic modular spaces by using fixed point ...
Murali Ramdoss, Divyakumari Pachaiyappan, Inho Hwang, Choonkil Park   +3 more
doaj   +1 more source

Functional inequalities for generalized multi-quadratic mappings

Journal of Inequalities and Applications, 2021
In 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.
Abasalt Bodaghi
doaj   +1 more source

On Jensen’s and the quadratic functional equations with involutions [PDF]

Proyecciones (Antofagasta), 2017
We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y),    x, y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Fadli, B., Chahbi, A., El-Fassi, Iz., Kabbaj, S.   +3 more
openaire   +3 more sources

On the Stability of Quadratic Functional Equations

Abstract and Applied Analysis, 2008
Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.
Lee, Jung Rye, An, Jong Su, Park, Choonkil   +2 more
openaire   +3 more sources

Fuzzy Stability of Quadratic Functional Equations [PDF]

Advances in Difference Equations, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dong Yun Shin, Choonkil Park, Sun-Young Jang, Jung Rye Lee   +3 more
openaire   +4 more sources

Jensen’s and the quadratic functional equations with an endomorphism [PDF]

Proyecciones (Antofagasta), 2017
We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x),    x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
openaire   +2 more sources