Sadia Khalid

On the refinements of the Jensen-Steffensen inequality

In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.2010 Mathematics Subject Classification. 26D15.

On the refinements of the integral Jensen-Steffensen inequality

In this paper, we present integral versions of some recently proved results which refine the Jensen-Steffensen inequality. We prove the n-exponential convexity and log-convexity of the functions associated with the linear functionals constructed from the refined inequalities and also prove the monotonicity property of the generalized Cauchy means. Finally, we give several examples of the families of functions for which the results can be applied.MSC:26A24, 26A48, 26A51, 26D15.

Improvement of Jensen's Inequality in terms of Gâteaux Derivatives for Convex Functions in Linear Spaces with Applications

In this paper, we prove some inequalities in terms of G^ateaux derivatives for convex functions dened on linear spaces and also give improvement of Jensens inequality. Furthermore, we give applications for norms, mean f-deviations and f-divergence mea- sures.

On the refinements of the Hermite-Hadamard inequality

In this paper, we present some refinements of the classical Hermite-Hadamard integral inequality for convex functions. Further, we give the concept of n-exponential convexity and log-convexity of the functions associated with the linear functionals defined by these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.MSC: 26D15.

Refinements of the Lower Bounds of the Jensen Functional

The lower bounds of the functional defined as the difference of the right-hand and the left-hand side of the Jensen inequality are studied. Refinements of some previously known results are given by applying results from the theory of majorization. Furthermore, some interesting special cases are considered.

Refinements of the majorization-type inequalities via green and fink identities and related results

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

Refinements and generalizations of majorization, Favard and Berwald-type inequalities via Fink identity

In this paper we present refinements of the majorization-type inequalities via an inequality obtained from a Fink’s identity as well as the refinements of the Favard-Berwald type inequalities by using monotonic sequence and positive weights.

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.