Analytic Inequalities

Analytic Inequalities by Dragoslav S. Mitrinovic.

The Theory of Inequalities began its development from the time when C. F. GACSS, A. L. CATCHY and P. L. CEBYSEY, to mention only the most important, laid the theoretical foundation for approximative meth­ ods. Around the end of the 19th and the beginning of the 20th century, numerous inequalities we...

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Bibliographic Details
Main Author: Mitrinovic, Dragoslav S. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1970.
Edition:1st ed. 1970.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 165
Springer eBook Collection.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Introduction
  • 1.1 Real Number System
  • 1.2 Complex Number System
  • 1.3 Monotone Functions
  • 1.4 Convex Functions
  • 2. General Inequalities
  • 2.1 Fundamental Inequalities
  • 2.2 Abel’s Inequality
  • 2.3 Jordan’s Inequality
  • 2.4 Bernoulli’s Inequality and its Generalizations
  • 2.5 ?ebyšev’s and Related Inequalities
  • 2.6 Cauchy’s and Related Inequalities
  • 2.7 Young’s Inequality
  • 2.8 Hölder’s Inequality
  • 2.9 Minkowski’s and Related Inequalities
  • 2.10 Inequalities of Aczél, Popoviciu, Kurepa and Bellman
  • 2.11 Schweitzer’s, Diaz-Metcalf’s, Rennie’s and Related Inequalities
  • 2.12 An Inequality of Fan and Todd
  • 2.13 Grüss’ Inequality
  • 2.14 Means
  • 2.15 Symmetric Means and Functions
  • 2.16 Steffensen’s and Related Inequalities
  • 2.17 Schur’s Inequality
  • 2.18 Turán’s Inequalities
  • 2.19 Benson’s Method
  • 2.20 Recurrent Inequalities of Redheffer
  • 2.21 Cyclic Inequalities
  • 2.22 Inequalities Involving Derivatives
  • 2.23 Integral Inequalities Involving Derivatives
  • 2.24 Inequalities Connected with Majorization of Vectors
  • 2.25 Inequalities for Vector Norms
  • 2.26 Mills Ratio and Some Related Results
  • 2.27 Stirling’s Formula
  • 3. Particular Inequalities
  • 3.1 Inequalities Involving Functions of Discrete Variables
  • 3.2 Inequalities Involving Algebraic Functions
  • 3.3 Inequalities Involving Polynomials
  • 3.4 Inequalities Involving Trigonometric Functions
  • 3.5 Inequalities Involving Trigonometric Polynomials
  • 3.6 Inequalities Involving Exponential, Logarithmic and Gamma Functions
  • 3.7 Integral Inequalities
  • 3.8 Inequalities in the Complex Domain
  • 3.9 Miscellaneous Inequalities
  • Name Index.

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