REVERSE OSTROWSKI'S TYPE WEIGHTED INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

In this paper we provide several upper and lower bounds for the Ostrowski difference 0 1 1 ) f (( 1 - t ) x + ty ) w ( t ) dt - 0 w ( t ) dt f (( 1 - lambda ) x + lambda y ), where f : C -> R is a convex function, C is a convex subset of a vector space X and w is integrable and nonnegative a.e. on [ 0 , 1 ] . A perturbed version under some natural assumptions on the weight function w is also considered. These results are then employed to obtain several weighted integral inequalities for norms and semi-inner products. The particular case of inner product spaces is analy & Oslash;and refinements of the weighted integral midpoint inequality for norms are provided.