Hermite–Hadamard type inequalities for twice differentiable generalized beta-preinvex functions via k-fractional integrals

Liko, Rozana and Kashuri, Artion (2023) Hermite–Hadamard type inequalities for twice differentiable generalized beta-preinvex functions via k-fractional integrals. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 34 (1). pp. 78-95. ISSN 1786-0091

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Abstract

In the present paper, a new class of generalized beta-preinvex function is introduced and some new integral inequalities for the left hand side of the Gauss–Jacobi type quadrature formula involving generalized beta-preinvex functions are given. Moreover, some Hermite–Hadamard type inequalities for generalized beta-preinvex functions that are twice differentiable via k-fractional integrals are established. At the end, some applications to special means are given. These general inequalities give us some new estimates for Hermite–Hadamard type k-fractional integral inequalities.

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