Abstract
This paper investigates the bounds of an integral operator for several kinds of convex functions. By applying definition of (<i>h - m</i>)-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 (<i>h - m</i>)-convex. Moreover a generalized Hadamard inequality for (<i>h - m</i>)-convex functions is proved by utilizing these operators. Also all the results are obtained for (<i>α, m</i>)-convex functions. Finally some applications of proved results are discussed.
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