Some new integral inequalities for (s, m)-convex and (α, m)-convex functions

Abstract

Some new integral inequalities for (s, m)-convex and (α, m)-convex functions The paper considers several new integral inequalities for functions the second derivatives of which, with respect to the absolute value, are (s, m)-convex and (α, m)-convex functions. These results are related to well-known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensen type inequality. In other words, new upper bounds for these inequalities using the indicated classes of convex functions have been obtained. These estimates are obtained using a direct definition for a convex function, classical integral inequalities of Hölder and power mean types. Along with the new outcomes, the paper presents results confirming the existing in literature upper bound estimates for integral inequalities (in particular well known in literature results obtained by U. Kırmacı in [7] and M.Z. Sarıkaya and N. Aktan in [35]). The last section presents some applications of the obtained estimates for special computing facilities (arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities).

Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

“…By summing I 1 and I 2 and taking into account Equation ( 12) and the notations, we get Equation (11). The proof is completed.…”

“…Many important inequalities have been established in the literature for various classes of convex functions and classes derived from them (for example, see [2,[9][10][11]).…”

Extensions of Ostrowski Type Inequalities via h -Integrals and s-Convexity

“…From the invention of (9), it is being studied extensively by many researchers (see [4][5][6][7][8][9]). Generalizations, extensions, and variants of this inequality exist in literature (see [10][11][12][13][14][15][16][17]) for different classes of convex functions.…”

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications

“…For more recent integral inequalities for the class of s-convex functions and its generalizations via di¤erent integral opertaors, one can consult [11,17,20,21,28,30,34].…”