New Perspectives on the Theory of Inequalities for Integral and Sum free ebook download.

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New Perspectives on the Theory of Inequalities for Integral and Sum free ebook download

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Author(s):	Nazia Irshad

Date:	2022	Format:	pdf	Language:	English	ISBN/ASIN:	3030905624
Pages:	319	OCR:		Quality:		ISBN13:
Uploader:	eternal	Upload Date:	3/18/2024 7:19:40 AM

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3030905624 pdf
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.

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Tags: Inequalities Integral Perspectives Theory

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