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1
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
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2019
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Vol. 25, nr 1
59--72
EN
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.
2
Content available remote Fractional integral inequalities for composite and k-composite preinvex functions
Kashuri A., Liko R., Iqbal S.
Fasciculi Mathematici
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2019
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nr 62
57--79
EN
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.
3
Content available remote Some new Hermite-Hadamard type inequalities via k-fractional integrals concerning differentiable generalized relative semi-(r; m, p, q, h1 , h2 ) -preinvex mappings
Kashuri A., Liko R.
Fasciculi Mathematici
|
2018
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Nr 60
59--78
EN
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.
4
Content available remote On Hermite-Hadamard type inequalities for functions whose first derivative absolute values are convex and concave
Qaisar S., Hussain S.
Fasciculi Mathematici
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2017
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Nr 58
155--166
EN
In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Corresponding error estimates for midpoint formula are also included. Moreover, some applications to special means of real numbers are also provided.
5
Content available remote Hermite-Hadamard type inequalities for MTm-preinvex functions
Kashuri A., Liko R.
Fasciculi Mathematici
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2017
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Nr 58
77--96
EN
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.
6
Content available remote 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
EN
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.
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