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A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions

Part of the Developments in Mathematics Book Series (volume 70)

DOI: 10.1007/978-3-030-95088-0

ISBN: 978-3-030-95087-3

Publisher: Springer International Publishing - Springer Journals

Mar 10, 2022

1 - 10 of 13 Chapters

Available

Introduction

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 1 –11

[Let ℝ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {R}_+$$...
Available

Preliminaries

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 13 –19

[This chapter is devoted to some basic definitions and results that are needed in this book. We essentially focus on the Newton interpolation theory and the higher order convexity and concavity properties.]
Available

Uniqueness and Existence Results

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 21 –31

[In this chapter, we establish Theorems 1.4 and 1.5 and show that, under the assumptions of these theorems, the sequence n↦fnp[g]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
Available

Interpretations of the Asymptotic Conditions

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 33 –43

[In this chapter, we study some important properties of the sets ℛSp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

Multiple logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\log \Gamma $$ \end{document}-Type Functions

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 45 –57

[In this chapter, we introduce and investigate the map, denote it by Σ, that carries any function g lying in ⋃p≥0(Dp∩Kp)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
Available

Asymptotic Analysis

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 59 –89

[The asymptotic behavior of the gamma function for large values of its argument can be summarized as follows: for any a ≥ 0, we have the following asymptotic equivalences (see Titchmarsh (The Theory of Functions, 2nd edn. Oxford University Press, Oxford, 1939, Section 1.87))...
Available

Derivatives of Multiple logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\log \Gamma $$ \end{document}-Type Functions

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 91 –110

[In this chapter, we discuss the higher order differentiability properties of Σg when g lies in Cr∩Dp∩Kmax{p,r}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
Available

Further Results

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 111 –160

[As discussed in the first chapter, the main objective of our work is to generalize Krull-Webster’s theory to multiple logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
Available

Summary of the Main Results

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 161 –177

[Now that we have collected a number of relevant results on multiple logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
Available

Applications to Some Standard Special Functions

Marichal, Jean-Luc; Zenaïdi, Naïm

Pages: 179 –254

[We now apply our results to certain multiple Γ-type functions and multiple logΓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...

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