Yazar "Hezenci, Fatih" seçeneğine göre listele

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    Advancements in corrected Euler-Maclaurin-type inequalities via conformable fractional integrals
    (Springer, 2025) Acar, Yaren; Budak, Huseyin; Bas, Umut; Hezenci, Fatih; Yildirim, Huseyin
    In this research article, equality is proved to obtain corrected Euler-Maclaurin-type inequalities. Using this identity, we establish several corrected Euler-Maclaurin-type inequalities for the case of differentiable convex functions by means of conformable fractional integrals. Moreover, some corrected Euler-Maclaurin-type inequalities are given for bounded functions by fractional integrals. Additionally, fractional corrected Euler-Maclaurin-type inequalities are constructed for Lipschitzian functions. Finally, corrected Euler-Maclaurin-type inequalities are considered by fractional integrals of bounded variation.
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    Advancements in Hermite-Hadamard inequalities via conformable fractional integrals for subadditive functions
    (World Scientific Publ Co Pte Ltd, 2025) Haider, Wali; Budak, Huseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, Haibo
    This study advances Hermite-Hadamard inequalities for subadditive functions using conformable fractional integrals. It establishes and explores numerous versions of these inequalities, as well as fractional integral inequalities for the product of two subadditive functions via conformable fractional integrals. The findings indicate that these inequalities improve and extend prior results for convex and subadditive functions, significantly enhancing the theoretical framework of fractional calculus and inequality theory. Moreover, computational analysis is conducted on these inequalities for subadditive functions, and mathematical examples are given to validate the newly established results within the framework of conformable fractional calculus.
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    Analysing Milne-type inequalities by using tempered fractional integrals
    (Springer Basel Ag, 2024) Haider, Wali; Budak, Huseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, Haibo
    In this research, we define an essential identity for differentiable functions in the framework of tempered fractional integral. By utilizing this identity, we deduce several modifications of fractional Milne-type inequalities. We provide novel expansions of Milne-type inequalities in the domain of tempered fractional integrals. The investigation emphasises important functional categories, including convex functions, bounded functions, Lipschitzian functions, and functions with bounded variation.
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    Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule
    (Mdpi, 2023) Budak, Hueseyin; Hezenci, Fatih; Kara, Hasan; Sarıkaya, Mehmet Zeki
    Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.
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    Bullen-type inequalities for twice-differentiable functions by using conformable fractional integrals
    (Springer, 2024) Hezenci, Fatih; Budak, Hueseyin
    In this paper, we prove an equality for twice-differentiable convex functions involving the conformable fractional integrals. Moreover, several Bullen-type inequalities are established for twice-differentiable functions. More precisely, conformable fractional integrals are used to derive such inequalities. Furthermore, sundry significant inequalities are obtained by taking advantage of the convexity, Holder inequality, and power-mean inequality. Finally, we provide our results by using special cases of obtained theorems.
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    Certain Simpson-type inequalities for twice-differentiable functions by conformable fractional integrals
    (Kangwon-Kyungki Mathematical Soc, 2023) Hezenci, Fatih; Budak, Hüseyin
    In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Fur-thermore, our results are provided by using special cases of obtained theorems.
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    A comprehensive study on Milne-type inequalities with tempered fractional integrals
    (Springer, 2024) Haider, Wali; Budak, Hüseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, Haibo
    In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.
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    Conformable fractional Newton-type inequalities with respect to differentiable convex functions
    (Springer, 2023) uenal, Cihan; Hezenci, Fatih; Budak, Hueseyin
    The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Holder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.
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    Conformable fractional versions of Hermite-Hadamard-type inequalities for twice-differentiable functions
    (Springer, 2023) Hezenci, Fatih; Kara, Hasan; Budak, Hüseyin
    In this paper, new inequalities for the left and right sides of the Hermite-Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems.
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    Error Bounds for Corrected Euler-Maclaurin Formula in Tempered Fractional Integrals
    (Global Science Press, 2025) Hezenci, Fatih; Budak, H¨Useyin
    In this paper, an equality is established for tempered fractional integrals. With the help of this equality, we prove several corrected Euler-Maclaurin-type inequalities for the case of differentiable convex functions involving tempered fractional integrals. Moreover, we provide our results by using special cases of obtained theorems. © 2025 Elsevier B.V., All rights reserved.
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    An extensive study on parameterized inequalities for conformable fractional integrals
    (Springer Basel Ag, 2023) Hezenci, Fatih; Budak, Hüseyin
    This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems.
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    Fractional Euler-Maclaurin-type inequalities for twice-differentiable functions
    (Springer, 2025) Shehzadi, Asia; Budak, Huseyin; Haider, Wali; Hezenci, Fatih; Chen, Haibo
    This article establishes a novel equality for twice-differentiable functions with convex absolute values in their second derivatives. This equality is used to establish Euler-Maclaurin-type inequalities through Riemann-Liouville fractional integrals. By utilizing convexity, the power mean inequality, and the H & ouml;lder inequality, several significant fractional inequalities can be derived. Moreover, the recently derived inequalities are not only grounded in theory but are also accompanied by concrete instances to further solidify their validity.
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    Fractional Euler-Maclaurin-type inequalities for various function classes
    (Springer Heidelberg, 2024) Hezenci, Fatih; Budak, Hüseyin
    This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation.
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    Fractional inequalities of corrected Euler-Maclaurin-type for twice-differentiable functions
    (Springer Heidelberg, 2023) Hezenci, Fatih
    In this article, an identity is proved for the case of twice-differentiable functions whose second derivatives in absolute value are convex. With the help of this equality, several corrected Euler-Maclaurin-type inequalities are established using the Riemann-Liouville fractional integrals. Several important fractional inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, the results are presented using special cases of obtained theories.
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    FRACTIONAL MACLAURIN-TYPE INEQUALITIES FOR TWICE-DIFFERENTIABLE FUNCTIONS
    (Rocky Mt Math Consortium, 2025) Hezenci, Fatih
    We prove an equality for twice-differentiable functions whose second derivatives in absolute value are convex. We use this, together with the H & ouml;lder and power-mean inequalities, to establish some Maclaurin-type inequalities for Riemann-Liouville fractional integrals. We conclude with some special cases.
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    Fractional midpoint-type inequalities for twice-differentiable functions
    (Univ Nis, Fac Sci Math, 2023) Hezenci, Fatih; Bohner, Martin; Budaka, Huseyin
    In this research article, we obtain an identity for twice differentiable functions whose second derivatives in absolute value are convex. By using this identity, we prove several left Hermite-Hadamard-type inequalities for the case of Riemann-Liouville fractional integrals. Furthermore, we provide our results by using special cases of obtained theorems.
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    Fractional Newton-type integral inequalities by means of various function classes
    (Wiley, 2024) Hezenci, Fatih; Budak, Hüseyin
    The authors of the paper present a method to examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, some fractional Newton-type inequalities are established by using convex functions. In addition, several fractional Newton-type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton-type inequalities for Lipschitzian functions. Furthermore, several Newton-type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.
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    Fractional Simpson-Type Inequalities for Twice Differentiable Functions
    (Univ Maragheh, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, Fatih
    In the literature, several papers are devoted to inequal-ities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on in-equalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.
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    Fractional trapezoid and newton type inequalities for differentiable s-convex functions
    (Honam Mathematical Soc, 2023) Hezenci, Fatih; Budak, Hüseyin; Ali, Muhammad Aamir
    In the present paper, we prove that our main inequality re-duces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.
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    Generalizations Euler-Maclaurin-type inequalities for conformable fractional integrals
    (Univ Nis, Fac Sci Math, 2025) Haider, Wali; Budak, Huseyin; Shehzadi, Asia; Hezenci, Fatih; Chen, Haibo
    In this study, we obtain a unique insight into differentiable convex functions by employing newly defined conformable fractional integrals. With this innovative approach, we unveil fresh Euler-Maclaurintype inequalities designed specifically for these integrals. Our proofs draw on fundamental mathematical principles, including convexity, Holder's inequality, and power mean inequality. Furthermore, we delve into new inequalities applicable to bounded functions, Lipschitzian functions, and functions of bounded variation. Notably, our findings align with established results under particular circumstances.