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

Sang Og Kim,John Michael Michael Rassias

doi:10.3390/math7111125

Sang Og Kim, John Michael Michael Rassias

Open Access

https://doi.org/10.3390/math7111125

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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.

Highlights

Introduction and PreliminariesThe research on modulars and modular spaces was begun by Nakano [1] as generalizations of normed spaces
We show the generalized Hyers-Ulam stability of Apollonius type additive functional equation from linear spaces to modular spaces
Putting φ ≡ ε > 0 in Theorem 2, we have the following result on classical Ulam stability of the Apollonius type additive functional equation

Summary

Introduction

Introduction and PreliminariesThe research on modulars and modular spaces was begun by Nakano [1] as generalizations of normed spaces. We show the generalized Hyers-Ulam stability of Apollonius type additive functional equation from linear spaces to modular spaces. Putting φ ≡ ε > 0 in Theorem 2, we have the following result on classical Ulam stability of the Apollonius type additive functional equation.

Results

Conclusion