Functional Equation
On the Superstability Related with the Trigonometric Functional Equation
... trigonometric functional equation from the following functional equations: fxy± gx−y λfxgy, fxy ±gx− y λgxfy, fxy ±gx−y λfxfy, fx y±gx−y λgxgy, which can be considered the mixed functional ...
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16. A quadratic type functional equation
... 𝑓 (𝑥 + 𝑦) + 𝑓 (𝑥 − 𝑦) = 2𝑓 (𝑥) + 2𝑓 (𝑦) (𝑥, 𝑦 ∈ 𝒳 ) (1.1) is called the quadratic functional equation. It is well known that a function 𝑓 between real vector spaces is quadratic if and only if there exists ...
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A pexider difference for a pexider functional equation
... RESEARCH Open Access A pexider difference for a pexider functional equation Abbas Najati1*, Saeid Ostadbashi2, Gwang Hui Kim3 and Sooran Mahmoudfakhe2 * Correspondence a nejati@yahoo com 1Department o[.] ...
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A Functional Equation of Aczél and Chung in Generalized Functions
... In this paper, by employing tensor products of regularizing functions as in 7, 8, we consider the regularity of the solutions of 1.3 and prove in an elementary way that 1.3 can be reduced to the classical equation ...
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Superstability of the functional equation with a cocycle related to distance measures
... type functional equation of (FE) added a cocycle property to the conditions in the results [, ...These functional equations arise in the characterization of symmetrically compositive sum-form ...
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Superstability and Stability of the Pexiderized Multiplicative Functional Equation
... the functional equation f x y f xfy was studied by Baker et ...a functional on a real vector space W satisfying |fx y − f xfy| ≤ δ for some fixed δ > 0 and all x, y ∈ W , then f is either bounded ...
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On a Functional Equation Related to Information Theory
... We would like to mention that Kannappan and Sahoo [3] have obtained the general solutions of (1.3) and (1.5) on an open domain. In our case, the process of finding the general solutions of (1.5), for fixed integers n ...
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Stability of an Additive Cubic Quartic Functional Equation
... equation. Every solution of the cubic functional equation is said to be a cubic mapping. Jun and Kim proved that a mapping f between two real vector spaces X and Y is a solution of 1.1 if and only if ...
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A new analogue of Gauss' functional equation
... The purpose of this paper is to obtain new results for the solution of 1.2 by following the theory on Gauss’ functional equation.. The main result is to solve 1.2 under suitable natural [r] ...
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Superstability of Some Pexider Type Functional Equation
... sine functional equation from the following Pexider- type functional equation fxygx−y λ·hxky λ : constant, which can be considered the mixed functional equation of the sine and ...
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Functional equation of a special Dirichlet series
... Dirichlet Series, Analytic Continuation, Functional Equation, F-Function.. 1980 AMS SUBJECT CLASSIFICATION CODE.[r] ...
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AQ-Functional Equation in Paranormed Spaces
... respectively satisfies the equations (1.1) and (1.2) . Recently J. M. Rassias and H.M.Kim [9] investigated Generalized Hyers-Ulam stability for general additive functional equations in quasi- β-normed spaces , ...
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On the approximate solution of Hosszus functional equation
... of Hyers’s stability Theorem which allows the Cauchy difference to be unbounded (see [4, 12, 14]). The stability problems of various functional equations ha been investigated by many authors (see [1, 2, 3, 4, 5, ...
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An AQCQ functional equation in paranormed spaces
... functional equation. In particular, every solution of the quadra- tic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof [21] for ...
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On the Stability of Quadratic Functional Equation
... various functional equations have been extensively investigated by a number of authors [1-3,6,9- ...11].The functional equation f(x+y)+f(x-y)=2f(x)+2f(y) is called a quadratic functional ...
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A Gauss type functional equation
... case n = 1 and p = log was studied in [2]. The essential step was done in [4] by the consideration of the definition (1.12) fo r n = 2 with an arbitrary p. The values n = −1 and n = 1 were studied in [5, 6]. The general ...
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The general solutions of a functional equation related to information theory
... The object of this paper is to investigate the general solutions of the functional equation (1.7) for fixed integers k ≥ 3 and ` ≥ 3. The corresponding results for the functional equations (1.8) and ...
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Stability of a functional equation connected with Reynolds operator
... stability of the functional equation F(x ◦ g(y)) – F(x)F(y) = 0 with bounded difference (Najdecki in J. Inequal. Appl. 2007:79816, 2007), we prove the stability of the above functional equation ...
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The C0 solutions of the Feigenbaum like functional equation
... Feigenbaum functional equation had been researched ...Feigenbaum’s equation as a singular Schroder functional equation whose solution was ob- tained using a scaling ansatz, and so ...
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An AQCQ functional equation in matrix Banach spaces
... quartic functional equation, and every solution of the quartic functional equation is said to be a quartic ...several functional equations have been extensively investigated by a number ...
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