Stability of a generalized trigonometric functional equation

Tongsomporn, Janyarak; Laohakosol, Vichian; Hengkrawit, Charinthip; Udomkavanich, Patanee

doi:10.1016/j.cam.2010.02.021

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Corollary 49 Let1

Introduction1

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Cited by 3 publications

(2 citation statements)

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“…The next result has been proved in [70]. The last presented theorem is the main result of [71] and includes a few outcomes from [72][73][74].…”

Section: Corollary 49 Letmentioning

confidence: 81%

Hyperstability and Superstability

Brzdęk

Ciepliński

2013

Abstract and Applied Analysis

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“…The next result has been proved in [70]. The last presented theorem is the main result of [71] and includes a few outcomes from [72][73][74].…”

Section: Corollary 49 Letmentioning

confidence: 81%

Hyperstability and Superstability

Brzdęk

Ciepliński

2013

Abstract and Applied Analysis

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“…which is so named because the two best known trigonometric functions, sine and cosine, are solutions of special cases of this equation. In [1], the authors investigated the stability of (1), where , , , and are nonzero functions from an abelian group ( , +) to the complex field C. Later in the same year, a generalized trigonometric functional equation with either the function or being bounded was investigated to complement the above earlier work where such function boundedness was not treated. A generalized quadratic functional equation is a functional equation of the form…”

Section: Introductionmentioning

confidence: 99%

Stability of a Generalized Trigonometric-Quadratic Functional Equation

Tongsomporn

Laohakosol

2013

Journal of Function Spaces and Applications

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A stability result for the generalized trigonometric-quadratic functional equation F(+)−G(−) = 2H()K()+L()+M() over the domain of a normed space and the range of a Banach space is derived. It states that under appropriate conditions on the function H()K(), the four functions F(), G(), L(), and M() are approximately equal to combinations of certain quadratic and additive functions. 1 , 2 , 3 , and 4 are functions from a normed space 1 to a Banach space 2. In the paper [7], the authors considered the stability of a combined generalized trigonometric-quadratic functional equation of the form F (+) + G (−) = 2H () K () + L () + M () (4) over the domain of an abelian group (, +) and the range C, except the control function whose range is taken to be the nonnegative real numbers [0, ∞). There, the functions H and K are explicitly determined under certain restrictions on the remaining functions F, G, L, and M. It is natural to ask whether the restrictions on the functions F, G, L, and M can be removed and/or altered to obtain some stability result of (4). We answer this question affirmatively using Jung's techniques elaborated in [6, 8].

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