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Journals / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 1

ON A FUNCTIONAL EQUATION ORIGINATING FROM A MIXED ADDITIVE AND CUBIC EQUATION AND ITS STABILITY

Mohammad JANFADAA
Tayebe Laal SHATERİB
Rahele SHOURVARZİC
Pages
27–41
Publication Date
2022-10-18
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Also the Hyers–Ulam–Rassias stability of this equation in thenon-Archimedean Banach spaces is investigated.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we study solutions of the 2-variable mixed additive andcubic functional equationf (2x + y, 2z + t) + f (2x − y, 2z − t) = 2f (x + y, z + t)+ 2f (x − y, z − t) + 2f (2x, 2z) − 4f (x, z),which has the cubic form f (x, y) = ax+ bx y + cxy+ dy as a solution.
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Key Findings & Data:In this paper, we study solutions of the 2-variable mixed additive andcubic functional equationf (2x + y, 2z + t) + f (2x − y, 2z − t) = 2f (x + y, z + t)+ 2f (x − y, z − t) + 2f (2x, 2z) − 4f (x, z),which has the cubic form f (x, y) = ax+ bx y + cxy+ dy as a solution.
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Conclusion & Impact:Also the Hyers–Ulam–Rassias stability of this equation in thenon-Archimedean Banach spaces is investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hyers–Ulam–Rassias stability · Cubic functional equation · Non–Archimedeannormed space

Abstract

In this paper, we study solutions of the 2-variable mixed additive andcubic functional equationf (2x + y, 2z + t) + f (2x − y, 2z − t) = 2f (x + y, z + t)+ 2f (x − y, z − t) + 2f (2x, 2z) − 4f (x, z),which has the cubic form f (x, y) = ax+ bx y + cxy+ dy as a solution. Also the Hyers–Ulam–Rassias stability of this equation in thenon-Archimedean Banach spaces is investigated.

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Cite This Article

JANFADAA, M., SHATERİB, T. L., SHOURVARZİC, R. (2022). ON A FUNCTIONAL EQUATION ORIGINATING FROM A MIXED ADDITIVE AND CUBIC EQUATION AND ITS STABILITY. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 1, 27–41. https://ajindex.com/articles/530350

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