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

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>&#916;</mo> <mn>2</mn>...

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Bibliographic Details
Main Authors: Sang Og Kim, John Michael Rassias
Format: Article
Language:English
Published: MDPI AG 2019-11-01
Series:Mathematics
Subjects:
hyers-ulam stability
fuzzy stability
apollonius type additive functional equation
modular space
δ<sub>2</sub>-condition
fuzzy banach space
Online Access:https://www.mdpi.com/2227-7390/7/11/1125
Description
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>&#916;</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>&#946;</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.
ISSN:2227-7390

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