A maximum theorem for generalized convex functions [PDF]
, 2022 Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions, i.e., for ...
PÁLES, Zsolt
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On the stability of an AQCQ-functional equation in random normed spaces [PDF]
, 2011 In this paper, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f ( x + 2 y ) + f ( x - 2 y ) = 4 f ( x + y ) + 4 f ( x - y ) - 6 f ( x ) (1) + f ( 2 y ) + f
Jang Sun Young +3 more
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Generalizations of an asymptotic stability theorem of Bahyrycz, Páles and Piszczek on Cauchy differences to generalized cocycles [PDF]
, 2018 We prove some straightforward analogues and generalizations of a re- cent asymptotic stability theorem of A. Bahyrycz, Zs. P´ales and M. Piszczek on Cauchy differences to semi-cocycles and pseudo-cocycles introduced in a former paper by the present ...
SZÁZ, Árpád, Árpád Száz
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Alienation of two general linear functional equations [PDF]
, 2020 We study the alienation problem for two general linear equations i.e. we compare the solutions of the system of equations n i=1 αif(pix + qiy) = 0 m j=1 βjg(sjx + tjy) = 0 with the solutions of the single equation n i=1 αif(pix + qiy) = m
Tomasz Szostok, Szostok, Tomasz
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On a modified Hyers‐Ulam stability of homogeneous equation
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 475-478, 1998., 1998 In this paper, a generalized Hyers‐Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx) − ykf(x)‖ ≤ φ(x, y) under suitable conditions, there exists a unique mapping T satisfying T(yx) = ytT(x) and ‖T(x) − f(x)‖ ≤ Φ(x).
Soon-Mo Jung
wiley +1 more source
New Pexiderizations of Drygas’ Functional Equation on Abelian Semigroups
Annales Mathematicae Silesianae, 2023 Let (S, +) be an abelian semigroup, let (H, +) be an abelian group which is uniquely 2-divisible, and let ϕ be an endomorphism of S. We find the solutions f, h : S → H of each of the functional equations f(x+y)+f(x+ϕ(y))=h(x)+f(y)+f∘ϕ(y), x,y∈S,f(x+y)+f ...
Aissi Youssef, Zeglami Driss
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Sine Subtraction Laws on Semigroups
Annales Mathematicae Silesianae, 2023 We consider two variants of the sine subtraction law on a semi-group S. The main objective is to solve f(xy∗ ) = f(x)g(y) − g(x)f(y) for unknown functions f, g : S → ℂ, where x ↦ x* is an anti-homomorphic involution.
Ebanks Bruce
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On a functional equation that has the quadratic-multiplicative property
Open Mathematics, 2020 In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil +4 more
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Stability of the second order partial differential equations [PDF]
, 2011 We say that a functional equation (ξ) is stable if any function g satisfying the functional equation (ξ) approximately is near to a true solution of (ξ).
M Eshaghi Gordji +3 more
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Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach [PDF]
, 2011 Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equation ...
Hassan Azadi Kenary +3 more
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