Exponential convexity for majorization
1 Department of Mathematics, University of Karachi, University Road, Karachi, Pakistan
2 Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3 Department of Mathematics, GC University, Faisalabad, Pakistan
4 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
Journal of Inequalities and Applications 2012, 2012:105 doi:10.1186/1029-242X-2012-105Published: 8 May 2012
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.