Exponential convexity for majorization

Journal of inequalities and applications

Asif R Khan¹ 

关键词: convex function;    majorization;    second-order divided difference;    positive semi-definite matrix;    exponential-convexity;    log-convexity;   

DOI  :  10.1186/1029-242X-2012-105

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we give more generalized results than in Anwar et al. (2010) and Latif and Pečarić (2010) in new direction by using second-order divided difference. We investigate the exponential convexity and logarithmic convexity for majorization type results by using class of continuous functions in linear functionals. We also construct positive semi-definite matrices for majorization type results. We will vary on choice of a family of functions in order to construct different examples of exponentially convex functions and construct some means. We also prove the monotonic property. Mathematics Subject Classification (2000): 26A51; 39B62; 26D15; 26D20; 26D99.

【 授权许可】

CC BY