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Fractional Hermite-Hadamard Inequalities

Jinrong Wang, Michal Fečkan (Autoren)

Buch | Hardcover

XII, 375 Seiten

2018
De Gruyter (Verlag)
978-3-11-052220-4 (ISBN)

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This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. ContentsIntroductionPreliminariesFractional integral identitiesHermite-Hadamard inequalities involving Riemann-Liouville fractional integralsHermite-Hadamard inequalities involving Hadamard fractional integrals

Jinrong Wang, Guizhou University, Guiyang, China; Michal Fečkan, Comenius University in Bratislava, Slovakia.

Table of Content:
Chapter 1 Introduction
1.1 Fractional Calculus via Application and Computation
1.2 Motivation of Fractional Hermite-Hadamard's Inequality
1.3 Main Contents
Chapter 2 Preliminaries
2.1 Definitions of Special Functions and Fractional Integrals
2.2 Definitions of Convex Functions
2.3 Singular Integrals via Series
2.4 Elementary Inequalities
Chapter 3 Fractional Integral Identities
3.1 Identities involving Riemann-Liouville Fractional Integrals
3.2 Identities involving Hadamard Fractional Integrals
Chapter 4 Hermite-Hadamard's inequalities involving Riemann-Liouville fractional integrals
4.1 Inequalities via Convex Functions
4.2 Inequalities via r-Convex Functions
4.3 Inequalities via s-Convex Functions
4.4 Inequalities via m-Convex Functions
4.5 Inequalities via (s, m)-convex Functions
4.6 Inequalities via Preinvex Convex Functions
4.7 Inequalities via (beta,m)-geometrically Convex Functions
4.8 Inequalities via geometrical-arithmetically s-Convex Functions
4.9 Inequalities via ( ,m)-logarithmically Convex Functions
4.10 Inequalities via s-GodunovaLevin functions
4.11 Inequalities via AG(log)-convex Functions
Chapter 5 Hermite-Hadamard's inequalities involving Hadamard fractional integrals
5.1 Inequalities via Convex Functions
5.2 Inequalities via s-e-ondition Functions
5.3 Inequalities via geometric-geometric co-ordinated Convex Function
5.4 Inequalities via Geometric-Geometric-Convex Functions
5.5 Inequalities via Geometric-Arithmetic-Convex Functions
References

Erscheinungsdatum	22.05.2018
Reihe/Serie	Fractional Calculus in Applied Sciences and Engineering ; 5
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	777 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik
Schlagworte	Applied • Applied mathematics • Differential Equations • Differential Equations and Dynamical Systems • Functional Analysis • Historiography • Jewish • Mathematics • Mathematik • MENDES-FLOHR • STJ102 • Technik • Ungleichungen
ISBN-10	3-11-052220-9 / 3110522209
ISBN-13	978-3-11-052220-4 / 9783110522204
Zustand	Neuware