Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces

Sang Og Kim and John Michael Rassias
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Sang Og Kim: School of Data Science, Hallym University, Chuncheon 24252, Korea
John Michael Rassias: Pedagogical Department of Education E.E., Mathematics and Informatics Section, National and Capodistrian University of Athens, 4, Agamemnonos St., Aghia Paraskevi, 15342 Athens, Greece

Mathematics, 2019, vol. 7, issue 11, 1-17

Abstract: In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without Δ 2 -conditions. We study the same problem in fuzzy Banach spaces and β -homogeneous Banach spaces. We show the hyperstability of the functional equation associated with the Jordan triple product in fuzzy Banach algebras. The obtained results can be applied to differential and integral equations with kernels of non-power types.

Keywords: Hyers-Ulam stability; fuzzy stability; Apollonius type additive functional equation; modular space; ? 2 -condition; fuzzy Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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