Yazar "Budak, Huseyin" seçeneğine göre listele

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    Approximating the Finite Mellin and Sumudu Transforms Utilizing Wavelet Transform
    (Univ Nis, Fac Sci Math, 2020) Usta, Fuat; Budak, Huseyin; Sarikaya, Mehmet Zeki
    In this study, some approximates for the finite Wavelet transform of different classes of absolutely continues mappings are presented using Wavelet transform of unit function. Then, with the help of these approximates, some other approximates for the finite Mellin and Sumudu transforms are given.
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    Certain fractional inequalities via the Caputo Fabrizio operator
    (Univ Nis, Fac Sci Math, 2023) Qaisar, Shahid; Munir, Arslan; Budak, Huseyin
    The Caputo Fabrizio fractional integral operator is one of the key concepts in fractional calculus. It is involved in many concrete and practical issues. In the present study, we have discussed some novel ideas to fractional Hermite-Hadamard inequalities within a Caputo Fabrizio fractional integral framework. The fractional integral under investigation is used to establish some new fractional Hermite-Hadamard inequalities. The findings of this study can be seen as a generalization and extension of numerous earlier inequalities via convex function. In addition, we demonstrate a few applications of our findings to special means of real numbers.
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    Certain Simpson-type inequalities for twice-differentiable functions by conformable fractional integrals
    (Kangwon-Kyungki Mathematical Soc, 2023) Hezenci, Fatih; Budak, Huseyin
    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, Huseyin; 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 versions of Hermite-Hadamard-type inequalities for twice-differentiable functions
    (Springer, 2023) Hezenci, Fatih; Kara, Hasan; Budak, Huseyin
    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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    Deriving weighted Newton-type inequalities for diverse function classes through Riemann-Liouville fractional integrals
    (Pergamon-Elsevier Science Ltd, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, Huseyin
    This study introduces weighted Newton-type inequalities for diverse function classes via Riemann-Liouville fractional integrals. We begin by employing a positive weighted function to demonstrate a crucial integral equality which necessary for establishing the main outcomes. Leveraging this equality along with Riemann- Liouville fractional integrals, we prove several weighted Newton-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. From the obtained results, one can get an insights into the implications of Newton-type inequalities and outlines potential avenues for future research endeavors.
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    Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities
    (Amer Inst Mathematical Sciences-Aims, 2023) Budak, Huseyin; Hyder, Abd-Allah
    In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.
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    Error Bounds for Fractional Integral Inequalities with Applications
    (Mdpi, 2024) Alqahtani, Nouf Abdulrahman; Qaisar, Shahid; Munir, Arslan; Naeem, Muhammad; Budak, Huseyin
    Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite-Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo-Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite-Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.
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    Extensions of Hermite-Hadamard inequalities for harmonically convex functions via generalized fractional integrals
    (Springer, 2021) You, Xue-Xiao; Ali, Muhammad Aamir; Budak, Huseyin; Agarwal, Praveen; Chu, Yu-Ming
    In the paper, the authors establish some new Hermite-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite-Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.
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    An extensive study on parameterized inequalities for conformable fractional integrals
    (Springer Basel Ag, 2023) Hezenci, Fatih; Budak, Huseyin
    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 various function classes
    (Springer Heidelberg, 2024) Hezenci, Fatih; Budak, Huseyin
    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 Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions
    (Univ Miskolc Inst Math, 2023) Ali, Muhammad Aamir; Soontharanon, Jarunee; Budak, Huseyin; Sitthiwirattham, Thanin; Feckan, Michal
    In this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Ho & BULL;lder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.
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    Fractional Hermite-Hadamard inequality, Simpson's and Ostrowski's type inequalities for convex functions with respect to a pair of functions
    (Rocky Mt Math Consortium, 2023) Xie, Jianqiang; Ali, Muhammad Aamir; Budak, Huseyin; Feckan, Michal; Sitthiwirattham, Thanin
    We consider the convexity with respect to a pair of functions and establish a Hermite-Hadamard type inequality for Riemann-Liouville fractional integrals. Moreover, we derive some new Simpson's and Ostrowski's type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.
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    FRACTIONAL HERMITE-HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS
    (Amer Mathematical Soc, 2020) Budak, Huseyin; Tunc, Tuba; Sarikaya, Mehmet Zeki
    In this paper, we define interval-valued right-sided Riemann-Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals.
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    Fractional Milne-type inequalities for twice differentiable functions
    (Amer Inst Mathematical Sciences-Aims, 2024) Almoneef, Areej A.; Hyder, Abd-Allah; Budak, Huseyin; Barakat, Mohamed A.
    In this study, a specific identity was derived for functions that possess two continuous derivatives. Through the utilization of this identity and Riemann-Liouville fractional integrals, several fractional Milne-type inequalities were established for functions whose second derivatives inside the absolute value are convex. Additionally, an example and a graphical representation are included to clarify the core findings of our research.
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    Fractional Newton-type integral inequalities by means of various function classes
    (Wiley, 2024) Hezenci, Fatih; Budak, Huseyin
    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 Ostrowski type inequalities for bounded functions
    (Springer, 2020) Erden, Samet; Budak, Huseyin; Zeki Sarikaya, Mehmet; Iftikhar, Sabah; Kumam, Poom
    We first establish some results involving Riemann-Liouville fractional integrals for partially differentiable functions. Then we obtain some fractional Ostrowski type inequalities for functions in class of functions Lp, L-infinity and L-1, respectively. We also give some midpoint type inequalities as special cases of our main results.
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    Fractional trapezoid and newton type inequalities for differentiable s-convex functions
    (Honam Mathematical Soc, 2023) Hezenci, Fatih; Budak, Huseyin; 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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    Further refinements and inequalities of Fejer's type via GA-convexity
    (Ramazan Yaman, 2024) Latif, Muhammad Amer; Budak, Huseyin; Kashuri, Artion
    In this study, we introduce some new mappings in connection with HermiteHadamard and Fejer type integral inequalities which have been proved using the GA-convex functions. As a consequence, we obtain certain new inequalities of the Fejer type that provide refinements of the Hermite-Hadamard and Fejer type integral inequalities that have already been obtained.
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    General (k, p)-Riemann-Liouville fractional integrals
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Budak, Huseyin
    The main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p which is determined over the (k, p)-gamma function. In particular, we present the harmonic, geometric and arithmetic (k, p)- Riemann-Liouville fractional integrals. When p = k, these integrals reduce to k-Riemann-Liouville fractional integrals. Some formulas relating to general (k, p)-Riemann-Liouville fraction integrals are also given.