M. Adil Khan

On Some Improvements of the Jensen Inequality with Some Applications

An improvement of the Jensen inequality for convex and monotone function is given as well as various applications for mean. Similar results for related inequalities of the Jensen type are also obtained. Also some applications of the Cauchy mean and the Jensen inequality are discussed.

Improvement and Reversion of Slater's Inequality and Related Results

We use an inequality given by Matić and Pečarić (2000) and obtain improvement and reverse of Slaters and related inequalities.

On the refinement of Jensen's inequality

The main purpose of this work is to present the extension of the recent results given by Dragomir S.S. Dragomir, A new refinement of Jensens inequality in linear spaces with applications, Math. Comput. Model. 52 (2010) 1497-1505], where new refinement of Jensens inequality is presented and given applications in the information theory. Our work improves the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to the Information Theory and obtained stronger lower bounds for the mean f-deviation and f-divergences.

Further Refinements of Jensen’s Type Inequalities for the Function Defined on the Rectangle

We give refinement of Jensen’s type inequalities given by Bakula and Pecaric (2006) for the co-ordinate convex function. Also we establish improvement of Jensen’s inequality for the convex function of two variables.

On a refinement of the majorisation type inequality

Abstract In this note, two mean value theorems are proved by using some recent results by Barnett et al. [N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals, Appl. Math. Lett. 22 (2009), 416-421]. A new class of Cauchy type means for two functions is studied. Logarithmic convexity for differences of power means is proved. Monotonicity of Cauchy means is shown.

The n-exponential convexity for majorization inequality for functions of two variables and related results

We apply the refined method of producing n -exponential convex functions of J. Pecaric and J. Peric to extend some known results on majorization type and related inequalities.