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Hermite-Hadamard type inequalities for MTm-preinvex functions

100%

Kashuri A. , Liko R.

Fasciculi Mathematici

2017

tom Nr 58

77--96

In the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MTm-preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These results not only extend the results appeared in the literature (see [13]), but also provide new estimates on these types.

Generalization of different type integral inequalities for generalized (s, m)-preinvex Godunova-Levin functions

100%

Kashuri A. , Liko R.

Journal of Applied Analysis

2018

tom Vol. 24, nr 2

211--221

In the present paper, the notion of generalized (s, m)-preinvex Godunova-Levin function of second kind is introduced, and some new integral inequalities involving generalized (s, m)-preinvex Godunova-Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite-Hadamard, Ostrowski and Simpson type inequalities for generalized (s, m)-preinvex Godunova-Levin functions of second kind via Riemann-Liouville fractional integral are established.

Some new Hermite-Hadamard type inequalities via k-fractional integrals concerning differentiable generalized relative semi-(r; m, p, q, h1 , h2 ) -preinvex mappings

100%

Kashuri A. , Liko R.

Fasciculi Mathematici

2018

tom Nr 60

59--78

In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r; m,p, q, h1, h2 )-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

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

100%

Kashuri A. , Liko R.

Fasciculi Mathematici

2017

tom 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.

Fractional integral inequalities for composite and k-composite preinvex functions

80%

Kashuri A. , Liko R. , Iqbal S.

Fasciculi Mathematici

2019

tom nr 62

57--79

In this article we found some Ostrowski inequalities for composite and k-composite preinvex functions via fractional integrals. Also some special cases will be given.