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1
Opial-type inequalities for conformable fractional integrals
Sarikaya Mehmet Zeki, Budak Hüseyin
Journal of Applied Analysis
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2019
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Vol. 25, nr 2
155--163
EN
In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.
2
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.
3
Generalized multivariate Fink-type identity and some related results on time scales with applications
Hussain Sabir, Latif Muhammad
Journal of Applied Analysis
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2019
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Vol. 25, nr 2
189--203
EN
Generalized Fink-type identity for multi-variables to an arbitrary time scales is obtained, giving some multi-variate Ostrowski, Iyengar and Grüss-type inequalities unifying the corresponding continuous and discrete version. Some new applications to generalized polynomials are also obtained.
4
Generalization of different type integral inequalities for generalized (s, m)-preinvex Godunova-Levin functions
Kashuri A., Liko R.
Journal of Applied Analysis
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2018
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Vol. 24, nr 2
211--221
EN
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.
5
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
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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.
6
Content available remote Some results for isotonic functionals via an inequality due to Kittaneh and Manasrah
Dragomir S. S.
Fasciculi Mathematici
|
2017
|
Nr 59
30--42
EN
In this paper we obtain some inequalities for isotonic functionals via a reverse and refinement of Young’s inequality due to Kittaneh and Manasrah.
7
Content available remote Hermite-Hadamard type inequalities for MTm-preinvex functions
Kashuri A., Liko R.
Fasciculi Mathematici
|
2017
|
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.
8
Content available remote On the zeros of an analytic function
Jain V.
Journal of Mathematics and Applications
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2014
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Vol. 37
51--58
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