Generalized convexity and inequalities involving special functions

DOI10.1016/J.JMAA.2007.03.008zbMath1132.52001OpenAlexW2042771280MaRDI QIDQ2381902

Song-Liang Qiu, Yu-Ming Chu, Xiao-Hui Zhang, Gen-Di Wang

Publication date: 26 September 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.03.008

zbMATH Keywords

generalized convexityGaussian hypergeometric functiongeneralized \(\eta\)-distortion functiongeneralized Grötzsch functionsub-multiplicativesuper-multiplicative

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Classical hypergeometric functions, ({}_2F_1) (33C05) Inequalities involving other types of functions (26D07)

Related Items (8)

Hölder concavity and inequalities for Jacobian elliptic functions ⋮ Topics in Special Functions III ⋮ On exterior moduli of quadrilaterals and special functions ⋮ On the generalized modulus ⋮ Concavity with respect to Hölder means involving the generalized Grötzsch function ⋮ The adjacent sides of hyperbolic Lambert quadrilaterals ⋮ Convexity with respect to Hölder mean involving zero-balanced hypergeometric functions ⋮ Sandor type fuzzy inequality based on the (\(s\), \(m\))-convex function in the second sense

Cites Work

• Generalized elliptic integrals and modular equations
• Inequalities for means
• Elliptic integral inequalities with applications
• Geometrically convex solutions of certain difference equations and generalized Bohr-Mollerup type theorems
• Approximate convexity and concavity of generalized Grötzsch ring function
• Generalized convexity and inequalities
• Functional Inequalities for Complete Elliptic Integrals and Their Ratios
• Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
• Landen inequalities for hypergeometric functions
• Convexity according to the geometric mean
• Inequalities for Zero-Balanced Hypergeometric Functions
• Duplication inequalities for the ratios of hypergeometric functions
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