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Summary:

This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters. In the first chapter, linear inequalities via interpolation polynomials and green functions are discussed. New results related to Popoviciu type linear inequalities via extension of the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials and the Fink identity with Green's functions, are presented. The second chapter is dedicated to Ostrowski's inequality and results with applications to numerical integration and probability theory. The third chapter deals with results involving functions with nondecreasing increments. Real life applications are discussed, as well as and connection of functions with nondecreasing increments together with many important concepts including arithmetic integral mean, wright convex functions, convex functions, nabla-convex functions, Jensen m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator of order m. The fourth chapter is mainly based on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this last chapter, the authors present results by using delta and nabla operators of higher order.

Table of Contents:

• 1 Linear Inequalities via Interpolation Polynomials and Green Functions
• 2 Ostrowski Inequality
• 3 Functions with Nondecreasing Increments
• 4 Popoviciu and Cebysev-Popoviciu Type Identities and Inequalities.

Author/Creator:

Irshad, Nazia , author

Contributors:

Khan, Asif R , author

Mehmood, Faraz , author

Pečarić, Josip , author

Languages:

English

Language Notes:

Item content: English

Main Work:

New Perspectives on the Theory of Inequalities for Integral and Sum [by Irshad, N.]

Subjects:

Functions of real variables

Difference equations

Functional equations

Physical Description:

XIII, 308 pages 2 illustrations in color : online resource.

Digital Characteristics:

text file

Call Numbers:

QA331.5 .I774 2021eb

ISBNs:

9783030905637
9788303090560 (7)

Other Standard Numbers:

Digital Object Identifier: 10.1007/978-3-030-90563-7

OCLC Numbers:

1374607547