Positive Gegenbauer polynomial sums and applications to starlike functions

Constructive Approximation

Volumn 23, Issue 2, 2006, Pages 197-210

  Koumandos, Stamatis ^a   Ruscheweyh, Stephan ^b  

^a UNIVERSITY OF CYPRUS   (Cyprus)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

Gegenbauer polynomials; Positive cosine sums; Starlike functions; Trigonometric inequalities

Indexed keywords

EID: 29644436169     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-004-0584-3     Document Type: Article

References (13)

1. G. E. ANDREWS, R. ASKEY, R. ROY (1999): Special Functions. Cambridge: Cambridge University Press.
2. N. K. BARY (1964): A Treatise on Trigonometric Series, Vol. I. Oxford: Pergamon Press.
3. A. S. BELOV (1995): Examples of trigonometric series with nonnegative partial sums. (Russian): Mat. Sb., 186:21-46.
4. (English translation) Mat. Sb., 186:485-510.
5. L. BRICKMAN, D. J. HALLENBECK, T. H. MACGREGOR, D. R. WILKEN (1973): Convex hulls and extreme points of families of starlike. and convex functions. Trans. Amer. Math. Soc., 185:413-428.
6. G. BROWN, S. KOUMANDOS, K. WANG (1996): Positivity of more Jacobi polynomial sums. Math. Proc. Cambridge Philos. Soc., 119:681-694.
7. G. BROWN, K.-Y. WANG, D. C. WILSON (1993): Positivity of some basic cosine sums. Math. Proc. Cambridge Philos. Soc., 114:383-391.
8. ST. RUSCHEWEYH (1982): Convolutions in Geometric Function Theory. Sém. Math. Sup., 83. Les Presses de l'Université de Montréal.
9. ST. RUSCHEWEYH, L. SALINAS (2000): On starlike functions of order μ ∈ [1/2, 1). Ann. Univ. Mariae Curie-Sklodowska, 54:117-123.
10. ST. RUSCHEWEYH, L. SALINAS (2004): Stable functions and Vietoris' theorem. J. Math. Anal. Appl., 291:596-604.
11. P. TURÀN (1953): Egy Steinhausfele problèmàrol. Mat. Lapok, 4:263-275.
12. W. H. YOUNG (1913): On a certain series of Fourier. Proc. London Math. Soc., 11:357-366.
13. A. ZYGMUND (1959): Trigonometric Series, 2nd ed. Cambridge: Cambridge University Press.