Fejer and Hermite–Hadamard type inequalities for superquadratic functions

Abstract

In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results.

Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

“…For more recent results which generalize, improve, and extend the inequalities presented above, one can see Abramovich et al [10], Cal et al [11], Avci et al [12], Odemir et al [13; 14], Dragomir [15; 16], Sarikaya et al [17], Xiao et al [18], Xi et al [19], Bessenyei [20], Tseng et al [21], Niculescu [22] and references therein.…”

Regularity of weakly subquadratic functions

“…(More precisely, in the paper above, superquadratic functions were considered, but here is an analogous relation between the concepts as above.) Subquadratic (or superquadratic) functions have been investigated by several authors in this sense (cf., e.g., [1,2,[4][5][6][8][9][10][11][12]18]). As a result of the study of the connection between the two different concepts of subquadraticity (cf.…”

Refinements of the Hermite–Hadamard Inequality in NPC Global Spaces

“…We would like to refer the reader to [10,2,16,21,19,13,1,22,6,3] and references therein for more information. In this paper we refine one side of H-H inequality in NPC global spaces via sequences.…”