# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## New generalizations of Jensen’s functional equationHTML articles powered by AMS MathViewer

by Hiroshi Haruki and Themistocles M. Rassias
Proc. Amer. Math. Soc. 123 (1995), 495-503 Request permission

## Abstract:

Let f be an unknown entire function of a complex variable, and let s, t be real variables. We consider Jensen’s functional equation $f\left ( {\frac {{x + y}}{2}} \right ) = \frac {{f(x) + f(y)}}{2},$ where x, y are complex variables. Replacing x and y by s and it in the above equation and taking the absolute values of the resulting equality one obtains the functional equation $\left | {f\left ( {\frac {{s + it}}{2}} \right )} \right | = \left | {\frac {{f(s) + f(it)}}{2}} \right |.$ The main purpose of this paper is to solve a new generalization of the above equation.
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