Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial

Journal of inequalities and applications

Ravi P Agarwal¹ 

关键词: majorization;    n-convexity;    Schur-convexity;    Sherman’s theorem;    Lidstone interpolating polynomial;    Čebyšev functional;    Grüss type inequalities;    Ostrowsky type inequalities;    exponentially convex functions;    log-convex functions;    means;    26D15;   

DOI  :  10.1186/s13660-015-0935-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In majorization theory, the well-known majorization theorem plays a very important role. A more general result was obtained by Sherman. In this paper, concerning 2n-convex functions, we get generalizations of these results applying Lidstone’s interpolating polynomials and the Čebyšev functional. Using the obtained results, we generate a new family of exponentially convex functions. The results are some new classes of two-parameter Cauchy type means.

【 授权许可】

CC BY