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1
Content available Analogy of classical and dynamic inequalities merging on time scales
Sahir Muhammad Jibril Shahab
Journal of Mathematics and Applications
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2020
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Vol. 43
139--152
EN
In this paper, we present analogues of Radon’s inequality and Nesbitt’s inequality on time scales. Furthermore, we find refinements of some classical inequalities such as Bergström’s inequality, the weighted power mean inequality, Cauchy–Schwarz’s inequality and Hölder’s inequality. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues.
2
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.
3
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.
4
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.
5
Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex
Meftah Badreddine
Journal of Applied Analysis
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2019
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Vol. 25, nr 2
165--171
EN
In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.
6
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.
7
Content available Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense
Budak H., Sarikaya M. Z., Set E.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
11-21
EN
In this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.
8
Content available remote More on Ostrowski type inequalities for some s-convex functions in the second sense
Liu Z.
Demonstratio Mathematica
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2016
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Vol. 49, nr 4
398--412
EN
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
9
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
10
Content available remote Some new generalizations of Maroni inequality on time scales
Yin L., Zhao C.
Demonstratio Mathematica
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2013
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Vol. 46, nr 4
645--654
EN
The aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.
11
Content available remote Some new factor theorem for absolute summability
Sulaiman W. T.
Demonstratio Mathematica
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2013
|
Vol. 46, nr 1
149--156
EN
A new general theorem concerning some kind of absolute summability is presented.
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