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2 Journal of Applied Analysis

2 2019

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On some k-fractional integral inequalities of Hermite-Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions

Kashuri Artion, Liko Rozana

Journal of Applied Analysis

2019

Vol. 25, nr 1

59--72

In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite-Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s, m, φ)-preinvex functions, Aust. J. Math. Anal. Appl. 13 (2016), no. 1, Article ID 16]. At the end, some applications to special means are given.

Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality

Meftah Badreddine

Journal of Applied Analysis

2019

Vol. 25, nr 1

83--90

In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.