New Perspectives on the Theory of Inequalities for Integral and Sum

This book discusses new inequalities for integral and sum, including results related to Popoviciu type linear inequalities, Ostrowskis inequality, functions with nondecreasing increments, and Popoviciu and Cebysev-Popoviciu type identities and inequalities. It also presents applications to numerical integration and probability theory.

Format: Paperback / softback
Length: 308 pages
Publication date: 31 March 2023
Publisher: Springer Nature Switzerland AG

This book is a valuable addition to the field of inequalities, particularly focusing on integral and sum inequalities. It comprises four chapters, each offering fresh insights into the theory.

In the first chapter, the authors delve into the realm of linear inequalities through the use of interpolation polynomials and green functions. They present novel results related to Popoviciu-type linear inequalities, extending the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials, and the Fink identity with Green's functions. These results showcase the power of these tools in solving inequality problems.

The second chapter is dedicated to Ostrowski's inequality, which finds applications in numerical integration and probability theory. The authors present various results related to Ostrowski's inequality, including those involving the Riemann sum and the integral transform. These results provide valuable tools for practitioners in these fields.

The third chapter explores the realm of functions with nondecreasing increments. The authors discuss real-life applications of these functions and their connection with important concepts such as the arithmetic integral mean, Wright convex functions, convex functions, nabla-convex functions, Jensen's m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, complete monotonic functions, Laplace transform, and exponentially convex functions. They employ the finite difference operator of order m to derive these results.

The fourth chapter primarily focuses on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this chapter, the authors present their findings by utilizing delta and nabla operators of higher order. These results add to the existing body of knowledge in the field and provide valuable insights for further research.

Overall, this book is a must-read for anyone interested in inequalities, particularly those working in integral and sum inequalities. The comprehensive coverage of topics and the use of modern mathematical techniques make it an invaluable resource for scholars and practitioners alike.

Weight: 498g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030905651
Edition number: 1st ed. 2021