General inequalities, consequences and applications

DOI10.1016/j.aam.2004.05.001zbMath1097.26015OpenAlexW2000487042WikidataQ55951342 ScholiaQ55951342MaRDI QIDQ1775728

Arcadii Z. Grinshpan

Publication date: 4 May 2005

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2004.05.001

zbMATH Keywords

beta functiongamma functionBernstein polynomialshypergeometric seriescombinatorial inequalitiesconvolutionsunivalent functionsfractional integralsbinomial coefficientsconfluent hypergeometric functionsintegral transformationsbi-Hermitian formsgeneral inequalitiespositive definite matrices and kernels

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Classical hypergeometric functions, ({}_2F_1) (33C05) Other analytical inequalities (26D20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items (15)

Volterra convolution equations: solution–kernel connection ⋮ Generalized hypergeometric functions: product identities and weighted norm inequalities ⋮ An inequality for multiple convolutions with respect to Dirichlet probability measure ⋮ Weighted norm inequalities for analytic functions ⋮ Inequalities for the gamma and \(q\)-gamma functions ⋮ Inequalities for gamma and q-gamma functions of complex arguments ⋮ An integral recursive inequality and applications ⋮ Weighted norm inequalities for convolutions, differential operators, and generalized hypergeometric functions ⋮ Weighted inequalities and negative binomials ⋮ Weighted integral and integro-differential inequalities ⋮ Formulas and Inequalities for Some Special Functions of a Complex Variable ⋮ Inequalities for formal power series and entire functions ⋮ Completely monotonic functions involving the gamma and $q$-gamma functions ⋮ A family of integral equations with restricted solutions ⋮ Integral inequalities for some special functions

Cites Work

• A proof of the Bieberbach conjecture
• Inequalities generated by the gamma function
• The Bieberbach Conjecture and Milin's Functionals
• Logarithmic coefficients means of univalent functions
• Coefficients of powers of univalent functions
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