Generalized inequalities for integral operators via several kinds of convex functions

Abstract

This paper investigates the bounds of an integral operator for several kinds of convex functions. By applying definition of (h - m)-convex function upper bounds of left sided (1.12) and right sided (1.13) integral operators are formulated which particularly provide upper bounds of various known conformable and fractional integrals. Further a modulus inequality is investigated for differentiable functions whose derivative in absolute value are (h - m)-convex. Moreover a generalized Hadamard inequality for (h - m)-convex functions is proved by utilizing these operators. Also all the results are obtained for (α, m)-convex functions. Finally some applications of proved results are discussed.

Keywords

• (<i>h - m</i>)-convex function
• (<i>α
• m</i>)-convex function
• integral operators
• fractional integral operators
• conformable integral operators