HERMITE-HADAMARD TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR TWICE DIFFERENTIABLE GENERALIZED (s, m, ϕ)-PREINVEX FUNCTIONS

Abstract

In the present paper, a new class of generalized $(s,m,\varphi)$-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized $(s,m,\varphi)$-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized $(s,m,\varphi)$-preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given.

Keywords

• Hermite-Hadamard type inequality
• H\"{o}lder's inequality
• power mean inequality
• Riemann-Liouville fractional integral
• $s$-convex function in the second sense
• $m$-invex
• $P$-function

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