On a conjecture for trigonometric sums and starlike functions

• Autores: Stamatis Koumandos, Stephan Ruscheweyh
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 149, Nº 1, 2007, págs. 42-58
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.04.006
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• Resumen

  • We pose and discuss the following conjecture: let , and for ?(0,1] let µ*(?) be the unique solution µ(0,1] of Then for 0<µµ*(?) and we have . We prove this for , and in a somewhat weaker form, for . Far reaching extensions of our conjectures and results to starlike functions of order 1-µ/2 are also discussed. Our work is closely related to recent investigations concerning the understanding and generalization of the celebrated Vietoris' inequalities.