Browsing by Author "Ardic, Merve Avci"

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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.