Log-convex solutions to the functional equation \(f(x+1)=g(x)f(x):\Gamma\)-type functions

DOI10.1006/jmaa.1997.5343zbMath0878.39004OpenAlexW2000212938MaRDI QIDQ1359637

Roger Webster

Publication date: 8 January 1998

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

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5343

zbMATH Keywords

gamma function\(q\)-gamma functionKrull's theoremlog-convex solutions

Mathematics Subject Classification ID

Functional equations for real functions (39B22) Gamma, beta and polygamma functions (33B15) Iteration theory, iterative and composite equations (39B12) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (15)

Spectral expansions of non-self-adjoint generalized Laguerre semigroups ⋮ Bernstein-gamma functions and exponential functionals of Lévy processes ⋮ Log-convex solutions of the second order to the functional equation \(f(x+1)=g(x)f(x)\) ⋮ Density solutions to a class of integro-differential equations ⋮ Remarks on the functional equation \(f(x+1) = g(x)f(x)\) and a uniqueness theorem for the gamma function ⋮ A generalization of Bohr-Mollerup's theorem for higher order convex functions: a tutorial ⋮ New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff's moment characterization theorem ⋮ On the law of homogeneous stable functionals ⋮ The log-Lévy moment problem via Berg–Urbanik semigroups ⋮ Turán inequalities and complete monotonicity for a class of entire functions ⋮ Analytic summability of real and complex functions ⋮ Upper bounds for analytic summand functions and related inequalities ⋮ Inequalities arising from generalized Euler-Type constants motivated by limit summability of functions ⋮ Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution ⋮ Geometrically convex solutions of a generalized gamma functional equation

Cites Work

• Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
• Theq-Gamma andq-Beta Functions†
• Another Proof that Convex Functions are Locally Lipschitz
• Subvex Functions and Bohr's Uniqueness Theorem
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
• On the convex solution of a certain functional equation
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