Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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STABILITY AND SOLUTION OF TWO FUNCTIONAL EQUATIONS IN UNITAL ALGEBRAS

  • Yamin Sayyari (Department of Mathematics, Sirjan University of Technology) ;
  • Mehdi Dehghanian (Department of Mathematics, Sirjan University of Technology) ;
  • Choonkil Park (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University)
  • Received : 2022.11.28
  • Accepted : 2023.07.22
  • Published : 2023.09.30
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Abstract

In this paper, we consider two functional equations: (1) h(𝓕(x, y, z) + 2x + y + z) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) + 2x + y) + h(xy) + yh(x + z) + 2h(z), (2) h(𝓕(x, y, z) - y + z + 2e) + 2h(x + y) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) - y + 2e) + 2h(x + y + z) + h(xy) + yh(x + z), without any regularity assumption for all x, y, z in a unital algebra A, where 𝓕 : A3 → A is defined by 𝓕(x, y, z) := h(x + y + z) - h(x + y) - h(z) for all x, y, z ∈ A. Also, we find general solutions of these equations in unital algebras. Finally, we prove the Hyers-Ulam stability of (1) and (2) in unital Banach algebras.

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References

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