Browsing by Author "Akdemir, Ahmet Ocak"

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Geometric-Harmonic Convexity and Integral Inequalities
(Amer inst Physics, 2016) Akdemir, Ahmet Ocak; Yalcin, Abdullatif; Polat, Fatma; Kavurmaci-Onalan, Havva
In this paper, some new integral inequalities have been proved for functions whose absolute value of derivatives are GH -convex functions by using integral equalities that have been obtained previously.
Inequalities of Bullen's Type for Logarithmically Convexity With Numerical Applications
(Springer international Publishing Ag, 2020) Kavurmaci-Onalan, Havva; Akdemir, Ahmet Ocak; Dutta, Hemen
In this study, we consider a familier inequality of Hermite-Hadamard inequality that is well known as Bullen's inequality in the literature. We remind an integral identity that derives Bullen's type integral inequalities. By using this integral identity, we have established new Bullen's type inequalities for functions whose second derivatives in absolute value are logarithmically convex. So, new error bounds for averaged midpoint-trapezoid quadrature rules are obtained and applications in numerical integration are given.
Integral Inequalities for Differentiable S-Convex Functions in the Second Sense Via Atangana-Baleanu Fractional Integral Operators
(Univ Nis, Fac Sci Math, 2023) Ardic, Merve Avci; Akdemir, Ahmet Ocak; Onalan, Havva Kavurmaci
Fractional integral operators, which form strong links between fractional analysis and integral inequalities, make unique contributions to the field of inequality theory due to their properties and strong kernel structures. In this context, the novelty brought to the field by the study can be expressed as the new and first findings of Ostrowski type that contain Atangana-Baleanu fractional integral operators for differentiable s-convex functions in the second sense. In the study, two new integral identities were estab-lished for Atangana-Baleanu fractional integral operators and by using these two new integral identities, Ostrowski type integral inequalities were obtained. In the findings, it was aimed to contribute to the field due to the structural properties of Atangana-Baleanu fractional integral operators.
New Approaches for M-Convex Functions Via Fractional Integral Operators With Strong Kernels
(Univ Miskolc inst Math, 2023) Ardic, Merve Avci; Onalan, Havva Kavurmaci; Akdemir, Ahmet Ocak; Nguyen, Anh Tuan
We have established this paper on m-convex functions, which can be expressed as a general form of the convex function concept. First of all, some inequalities of Hadamard type are proved with fairly simple conditions. Next, an integral identity containing Atangana-Baleanu fractional integral operators is obtained to prove new inequalities for differentiable m -convex functions. Using this identity, various properties of m-convex functions and classical inequalities, some new integral inequalities have been proved.
On New General Versions of Hermite-Hadamard Type Integral Inequalities Via Fractional Integral Operators With Mittag-Leffler Kernel
(Springer, 2021) Kavurmaci onalan, Havva; Akdemir, Ahmet Ocak; Avci Ardic, Merve; Baleanu, Dumitru
The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite-Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Holder's inequality and Young's inequality, are taken into account in the proof of the findings.