Naveed Latif

Some New Results Related to Favard's Inequality

Log-convexity of Favards difference is proved, and Dreschers and Lyapunovs type inequalities for this difference are deduced. The weighted case is also considered. Related Cauchy type means are defined, and some basic properties are given.

Exponential convexity for majorization

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.

Cauchy Means of the Popoviciu Type

We discuss log-convexity for the differences of the Popoviciu inequalities and introduce some mean value theorems and related results. Also we give the Cauchy means of the Popoviciu type and we show that these means are monotonic.

Positive Semidefinite Matrices, Exponential Convexity for Majorization, and Related Cauchy Means

We prove positive semidefiniteness of matrices generated by differences deduced from majorization-type results which implies exponential convexity and log-convexity of these differences and also obtain Lyapunovs and Dreshers inequalities for these differences. We introduce new Cauchy means and show that these means are monotone.

Generalized results of majorization inequality via Lidstone's polynomial and newly Green functions

Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pecari ˇ c, J. Inequal. Appl., ´ 2017 (2017), 17 pages] and Lidstone’s polynomial. We find new upper bounds of Gruss and Ostrowski type. We give further results of majorization inequality by making linear functionals constructed on ¨ convex functions. Some applications are given.