Applied Mathematics & Information Sciences

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In this work, we introduce a new class of harmonically convex functions, namely, generalized harmonically ψ-MT-convex functions established on fractal set techniques, for establishing inequalities of Hermite-Hadamard type and certain related variants with respect to the Raina’s function. With the help of an auxiliary identity associated with Raina’s function, by generalized Holder inequality and generalized power mean, generalized midpoint type, Ostrowski type, and trapezoid type inequalities via local fractional integral for generalized harmonically ψ-MT-convex functions are given. The introduced technique gives the results by establishing some special values for the parameters or applying restrictive suppositions and is entirely practicable for regaining the existing inequalities in the related literature.

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