On some inequalities for s-convex functions and applications

Abstract

Some new results related to the left-hand side of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives at certain powers are s-convex functions in the second sense are obtained. Also, some applications to special means of real numbers are provided. MSC: Primary 26A51; 26D15

Hermite–Hadamard-type inequalities for functions whose derivatives are η-convex via fractional integrals

“…If we take q = 1 in Corollary 3.5, then we get Corollary 3.3. To prove our next results, we consider the following lemma proved in [10].…”

“…Xi and Qi [9], Ozdemir et al [10], and Sarikaya et al [5] established Hermite-Hadamardtype inequalities for convex functions. Gordji et al [11] introduced an important generalization of convexity known as η-convexity.…”

Hadamard type local fractional integral inequalities for generalized harmonically convex functions and applications

“…In recent years, due to the generalization of the definition of convexity, many new results have been obtained in the study of Hermite‐Hadamard's inequality. Readers can refer to and the references therein.…”

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“…We note that Hadamards inequality may be regarded as a refinement of the concept of convexity and it follows easily from Jensens inequality. Hadamards inequality for convex functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found (see, for example, [2], [5], [11], [16], [18]) and the references cited therein.…”