ON SHERMAN'S TYPE INEQUALITIES FOR n-CONVEX FUNCTION WITH APPLICATIONS

Abstract

New generalizations of Sherman's inequality for convex functions of higher order are obtained by using Hermite's interpolating polynomials and Green's function. The Ostrowski and Gruss type bounds for the identity related to generalized Sherman's inequality are established. Some applications are discussed.

Keywords

• majorization,n-convexity,Schur-convexity,Sherman's theorem,Hermite's interpolating polynomial,Cebysev functional,Gruss type inequalities,Ostrowsky-type inequalities,exponentially convex functions,log-convex functions,means

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