A Kannappan-sine addition law on semigroups

TL;DR

This paper investigates the solutions to a specific functional equation called the Kannappan-sine addition law within semigroups, providing a comprehensive characterization of these solutions.

Contribution

It characterizes the complex-valued solutions of the Kannappan-sine addition law on semigroups, extending understanding of functional equations in algebraic structures.

Findings

Explicit solutions for the functional equation are derived.

The solutions depend on the structure of the semigroup and the fixed element.

The work generalizes previous results on similar functional equations.

Abstract

Let $S$ be a semigroup and $z_{0}$ a fixed element in $S.$ We determine the complex-valued solutions of the following Kannappan-sine addition law $f(xyz_{0})=f(x)g(y)+f(y)g(x),x,y\in S.$