Sine and cosine equations on commutative hypergroups
\.Zywilla Fechner, L\'aszl\'o Sz\'ekelyhidi
TL;DR
This paper investigates the solutions to functional equations representing sine and cosine addition theorems within the context of commutative hypergroups, extending classical trigonometric identities to a more general algebraic setting.
Contribution
It characterizes solutions of sine and cosine addition equations on commutative hypergroups, a novel extension of classical trigonometric identities.
Findings
Solutions are explicitly characterized for the hypergroup setting.
The work generalizes classical addition formulas to algebraic structures beyond groups.
Provides a foundation for further harmonic analysis on hypergroups.
Abstract
In this paper we describe the solutions of the functional equations expressing the addition theorems for sine and cosine on commutative hypergroups.
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Taxonomy
TopicsFunctional Equations Stability Results · Fuzzy and Soft Set Theory