General inequalities, consequences and applications

Advances in Applied Mathematics

Volumn 34, Issue 1, 2005, Pages 71-100

  Grinshpan, Arcadii Z ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Bernstein polynomials; Beta function; Bi hermitian forms; Binomial coefficients; Combinatorial inequalities; Confluent hypergeometric functions; Convolutions; Exponentiation; Fractional integrals; Gamma function; General inequalities; General polynomials; Hypergeometric series; Integral transformations; Positive definite matrices and kernels; Univalent functions

Indexed keywords

COMBINATORIAL MATHEMATICS; CONVOLUTION; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; POLYNOMIALS; VECTORS;

BERNSTEIN POLYNOMIALS; BETA FUNCTION; BINOMIAL COEFFICIENTS; COMBINATORIAL INEQUALITIES; CONFLUENT HYPERGEOMETRIC FUNCTIONS; FRACTIONAL INTEGRALS; GAMMA FUNCTION; GENERAL INEQUALITIES; HYPERGEOMETRIC SERIES; INTEGRAL TRANSFORMATIONS;

COMPUTATION THEORY;

EID: 10244251660     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aam.2004.05.001     Document Type: Article

References (20)

1. G.E. Andrews, R. Askey, R. Roy, Special Functions, Encyclopedia Math. Appl., vol. 71, Cambridge University Press, Cambridge, 1999.
2. E.F. Beckenbach, R.E. Bellman, Inequalities, Springer, Berlin, 1961.
3. P. Borwein, T. Erdélyi, Polynomials and Polynomial Inequalities, Springer, New York, 1995.
4. L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985) 137-152.
5. B.C. Carlson, Special Functions of Applied Mathematics, Academic Press, New York, 1977.
6. A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Triconi, Higher Transcendental Functions, vol. 1, Krieger, New York, 1981.
7. A.Z. Grinshpan, The Bieberbach conjecture and Milin's functionals, Amer. Math. Monthly 106 (3) (1999) 203-214.
8. A.Z. Grinshpan, Inequalities generated by the gamma function, Adv. in Appl. Math. 29 (1) (2002) 115-125.
9. A.Z. Grinshpan, Logarithmic geometry, exponentiation, and coefficient bounds in the theory of univalent functions and nonoverlapping domains, in: R. Kühnau (Ed.), Handbook of Complex Analysis, vol. 1: Geometric Function Theory, North-Holland, Amsterdam, 2002, pp. 273-332.
10. A.Z. Grinshpan, M.E.H. Ismail, Completely monotonic functions involving the gamma function and its q-analogue, preprint, 2004.
11. A.Z. Grinhspan, Ch. Pommerenke, The Grunsky operator and coefficient differences, Complex Variables 33 (1997) 113-127.
12. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, 2nd ed., University Press, Cambridge, 1952.
13. W.K. Hayman, J.A. Hummel, Coefficients of powers of univalent functions, Complex Variables 7 (1986) 51-70.
14. G.G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.
15. I.M. Milin, On the coefficients of univalent functions, Dok]. Akad. Nauk SSSR 176 (1967) 1015-1018 (in Russian);
16. I.M. Milin, Soviet Math. Dok]. 8 (1967) 1255-1258.
17. I.M. Milin, Univalent Functions and Orthonormal Systems, Nauka, Moscow, 1971 (in Russian); published in English by Amer. Math. Soc., Providence, RI, 1977.
18. I.M. Milin, A.Z. Grinshpan, Logarithmic coefficients means of univalent functions, Complex Variables 7 (1986) 139-147.
19. I.P. Natanson, Theory of Functions of a Real Variable, vol. 1, Frederick Ungar, New York, 1961.
20. A.I. Zayed, Handbook of Function and Generalized Function Transformations, CRC Press, Boca Raton, 1996.