Boundedness of approximate trigonometric functions

doi:10.1016/j.aml.2008.06.013

Applied Mathematics Letters

Volume 22, Issue 4, April 2009, Pages 439-443

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Abstract

In this work, we prove that approximate trigonometric functions are bounded. That is, if a non-zero function $f$ satisfies the inequality $| f (x + y) - f (x - y) - 2 f (x) f (y) | \leq φ (x)$ or $φ (y)$ , then $f$ is bounded.

Keywords

Alembert equation

Sine functional equation

Trigonometric functional equation

Functional inequality