SOME OSTROWSKI TYPE INEQUALITIES FOR Π-Τιμε DIFFERENTIABLE MAPPINGS AND APPLICATIONS

Some new integral inequalities for n-times differentiable convex and concave functions

“…The classical Hermite-Hadamard inequality provides estimates of the mean value of a continuous convex or concave function. Hadamard's inequality for convex or concave functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found; for example see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A function f : I ⊆ R → R is said to be convex if the inequality f (tx + (1 − t)y) tf (x) + (1 − t)f (y) , is valid for all x, y ∈ I and t ∈ [0, 1].…”

“…Convexity theory has appeared as a powerful technique to study a wide class of unrelated problems in pure and applied sciences. For some inequalities, generalizations and applications concerning convexity see [3,[5][6][7][8][9][10][11][15][16][17][18]. Recently, in the literature there are so many papers about n-times differentiable functions on several kinds of convexities.…”

Some new integral inequalities for n-times differentiable log-convex functions

“…Recently, in the literature there are so many papers about n-times differentiable functions on several kinds of convexities. In references [3,4,5,8,12,13,17,19], readers can find some results about this issue. Many papers have been written by a number of mathematicians concerning inequalities for different classes of log-convex functions see for instance the recent papers [1,2,7,14,15,16,18,20] and the references within these papers.…”

Derivation and applications of inequalities of Ostrowski type for n-times differentiable mappings for cumulative distribution function and some quadrature rules

“…Some of the classical inequalities for means can be derived from [2] for particular choices of the function f. Many researchers have given considerable attention to the inequality (1.1) and its various generalizations, have appeared in the literature, to mention a few, see [1,4,5,6,8,9,10,11,13,16,20,21] and the references cited therein.…”