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.
General
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