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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.

Hermite-Hadamard type fractional integral inequalities for generalized (r; g,s,m,φ)-preinvex functions

Kashuri A., Liko R.

Fasciculi Mathematici

2017

Nr 59

43--55

In the present paper, a new class of generalized (r; g, s, m, ϕ)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (r; g, s, m, ϕ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized (r; g, s, m, ϕ)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1],[2]), but also provide new estimates on these types.

The Hadamard inequalities for s-convex functions in the second sense

Dragomir S., Fitzpatrick S.

Demonstratio Mathematica

1999

Vol. 32, nr 4

687-696

We derive some inequalities of Hadamard's type for s-convex functions in the second sense and give some applications connected with special means.