A note on a functional inequality

Horst Alzer

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-3

Abstract:

We prove: If r 1 , … , r k are (fixed) positive real numbers with ∏ j = 1 k r j > 1 , then the only entire solutions φ : ℂ → ℂ of the functional inequality ∏ j = 1 k | φ ( r j z ) | ≥ ( ∏ j = 1 k r j ) | φ ( z ) | k are φ ( z ) = c z n , where c is a complex number and n is a positive integer.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:130245

DOI: 10.1155/S0161171292000553

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