A functional equation

V. S. Kozyakin

Voronezh State University

Abstract: Existence theorems for and the determination of continuous solutions, defined on the real axis $R$, of the functional equation $f(t)=A[t,f(at-b),f(at-c)]$, where $a$, $b$ and $c$ are real parameters, $A: R\times E\times E\to E$ is a continuous operator, and $E$ is a Banach space.

UDC: 513.88

Received: 26.11.1969

 English version: Mathematical Notes, 1971, 9:2, 95–100

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