Stability of the Apollonius Type Additive Functional Equation in Modular Spaces and Fuzzy Banach Spaces
In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without <inline-formula> <math display="inline"> <semantics> <msub> <mo>Δ</mo> <mn>2</mn>...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
MDPI AG
2019-11-01
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Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/7/11/1125 |
Summary: | In this work, we investigate the generalized Hyers-Ulam stability of the Apollonius type additive functional equation in modular spaces with or without <inline-formula> <math display="inline"> <semantics> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-conditions. We study the same problem in fuzzy Banach spaces and <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-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. |
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ISSN: | 2227-7390 |