Stability and Solution of Functional Equations

Dear Colleagues,

Expressing social and physical rules as a function is an important part of functional analysis.

It is a very valuable to research into stability, for which there exists a functional equation near an approximate functional equation. It is also important to find the solution of an unknown functional equation and to investigate the inequality relationship between the functional equations.

In 1940, S.M. Ulam conjectured the stability problem of the function equation as above. Its conjecture was shown by Hyers and improved by Bourgin, Aoki and Rassias, etc.

This research took off in three directions, which are the development of a proof method of stability, changing to various domains, and the finding of its solution type for the known–unknown functional equation.

The purpose of this Special Issue is to help research in this field by gathering the latest results, which are the stability and solution of the known–unknown functional equation, the difference equation, and changing to various domains.

For this Special Issue, we would like to invite original research and review articles including the following:

1) Improvement and development of stability for functional equations: Hyers–Ulam stability, generalized Hyers–Ulam stability (in the sense of Gavruta and Ger), superstability, hyperstability, fixed point method, etc.;

2) Creation and discovery of the known–unknown functional equation: basic (fundamental) functional equation, trigonometric functional equation, transcendental functional equation, differential equation, Euler–Lagrange equation, homomorphism, derivation;

3) In various domains: (semi-)group, vector space, real–complex number set, Banach algebra, C* -algebra, restricted domain, etc.

Prof. Dr. Gwang Hui Kim
Prof. Dr. Choonkil Park
Guest Editors

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• Stability
• Hyers–Ulam stability
• Generalized Hyers–Ulam stability
• Superstability
• Hyperstability
• Fixed point method
• Solution of functional equation
• Functional inequality
• Trigonometric functional equation (cosine, sine)
• Difference equation
• Nonlinear differential equation
• Euler–Lagrange equation
• Operator equation
• (Bi-)homomorphism
• (Bi-)derivation
• Banach algebra
• C* -algebra
• Ternary algebra