engleski

Generalizations and refinements of Hardy's inequality

In this thesis an integral operator with general non-negative kernel on measure spaces with positive measure is considered and some new weighted Hardy type inequalities for convex functions and refinements of weighted Hardy type inequalities for superquadratic functions have been obtained. Moreover, some refinements of weighted Hardy type inequalities for convex functions and some new refinements of discrete Hardy type inequalities are given. Furthermore, improvements and reverses of new weighted Hardy type inequalities with integral operators are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.

The Hardy inequality; he Hilbert inequality; Inequalities; Hardy type inequalities; convex function; kernel; The Hardy operator with general kernel

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