Yazar "Budak, Huseyin" 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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    Bullen-Mercer type inequalities for the h-convex function with twice differentiable functions
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Huseyin
    Bullen-type inequalities for h-convex functions using conformable fractional operators are established in this study on the cone of twice-differentiable functions. This is a novel fractional version of the existing Bullen-type inequalities with simple procedures using the B-function. Furthermore, new results on Bullen-type inequalities are presented for several specific cases of convexity, generalizing existing inequalities known in the literature.
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    Development of Fractional Newton-Type Inequalities Through Extended Integral Operators
    (Mdpi, 2025) Hyder, Abd-Allah; Almoneef, Areej A.; Barakat, Mohamed A.; Budak, Huseyin; Aktas, Ozge
    This paper introduces a new class of Newton-type inequalities (NTIs) within the framework of extended fractional integral operators. This study begins by establishing a fundamental identity for generalized fractional Riemann-Liouville (FR-L) operators, which forms the basis for deriving various inequalities under different assumptions on the integrand. In particular, fractional counterparts of the classical 1/3 and 3/8 Simpson rules are obtained when the modulus of the first derivative is convex. The analysis is further extended to include functions that satisfy a Lipschitz condition or have bounded first derivatives. Moreover, an additional NTI is presented for functions of bounded variation, expressed in terms of their total variation. In all scenarios, the proposed results reduce to classical inequalities when the fractional parameters are specified accordingly, thus offering a unified perspective on numerical integration through fractional operators.
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    Exploring error estimates of Newton-Cotes quadrature rules across diverse function classes
    (Springer, 2025) Lakhdari, Abdelghani; Awan, Muhammad Uzair; Dragomir, Silvestru Sever; Budak, Huseyin; Meftah, Badreddine
    This in-depth study looks at symmetric four-point Newton-Cotes-type inequalities with a focus on error estimates for numerical integration. The precision of these estimates is explored across various classes of functions, including those with bounded variation, bounded derivatives, Lipschitzian derivatives, convex derivatives, and others. The research synthesizes and extends existing knowledge, providing a nuanced understanding of how error bounds depend on the characteristics of integrated functions. Through a systematic review of seminal works, the study contributes to the practical application of numerical integration techniques, offering insight for researchers and practitioners to make informed choices based on the specific features of the functions involved.
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    Extension of Milne-type inequalities to Katugampola fractional integrals
    (Springer, 2024) Lakhdari, Abdelghani; Budak, Huseyin; Awan, Muhammad Uzair; Meftah, Badreddine
    This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.
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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 Milne-type inequalities for twice differentiable functions for Riemann-Liouville fractional integrals
    (Springer Basel Ag, 2024) Haider, Wali; Budak, Huseyin; Shehzadi, Asia
    In this research, we investigate the error bounds associated with Milne's formula, a well-known open Newton-Cotes approach, initially focused on differentiable convex functions within the frameworks of fractional calculus. Building on this work, we investigate fractional Milne-type inequalities, focusing on their application to the more refined class of twice-differentiable convex functions. This study effectively presents an identity involving twice differentiable functions and Riemann-Liouville fractional integrals. Using this newly established identity, we established error bounds for Milne's formula in fractional and classical calculus. This study emphasizes the significance of convexity principles and incorporates the use of the H & ouml;lder inequality in formulating novel inequalities. In addition, we present precise mathematical illustrations to showcase the accuracy of the recently established bounds for Milne's formula.
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    GENERAL ((k, p ) , ψ)-HILFER FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2024) Benaissa, Bouharket; Budak, Huseyin
    The main motivation of this study is to establish a general version of the RiemannLiouville fractional integrals with two exponential parameters k and p called ((k, p),psi)-Hilfer fractional integrals which is determined over the k-gamma function. We first prove that these operators are well-defined, continuous and have semi-group property. Then, particularly, we present the harmonic, geometric and arithmetic (k, p), psi-Hilfer fractional integrals. Moreover, some special cases relating to general ((k, p),psi)-Riemann-Liouville fraction integrals are given.
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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.
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    Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions
    (Mdpi, 2025) Almoneef, Areej A.; Hyder, Abd-Allah; Hezenci, Fatih; Budak, Huseyin
    This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite-Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis.
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    Generalized local fractional integral inequalities via generalized (h1,h2)-preinvexity on fractal sets
    (World Scientific Publ Co Pte Ltd, 2025) Al-Sa'di, Sa'ud; Bibi, Maria; Muddassar, Muhammad; Budak, Huseyin
    In this paper, we establish several general local fractional integral inequalities via generalized (h1,h2) preinvex mapping on fractal sets. By considering different parameter values, we develop particular applications of our result, such as midpoint-type inequality, generalized trapezoidal-type inequality, and generalized Simpson-type inequality. We present applications of the derived inequalities in numerical quadrature formulas, providing error estimates.
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    Hermite-Hadamard inequalities for left fractional conformable integral operator
    (Springer, 2025) Budak, Huseyin; Ozmen, Nejla
    In this paper, we first establish the Hermite-Hadamard inequality for left fractional conformable integral operators. Then, we present an example and a graph to illustrate the obtained Hermite-Hadamard inequalities. Moreover, we also present several corresponding trapezoid and midpoint inequalities. For this aim, we first prove two identities for differentiable functions. By using these equalities, we establish some trapezoid- and midpoint-type inequalities for convex functions. Furthermore, we present several remarks to give the relation between the obtained results in this paper and earlier ones.
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    HERMITE-HADAMARD TYPE INEQUALITIES FOR PREINVEX FUNCTIONS WITH APPLICATIONS
    (Kangwon-Kyungki Mathematical Soc, 2025) Singh, Shiwani; Mishra, Shashi kant; Singh, Vandana; Kumar, Pankaj; Budak, Huseyin
    In this article, we establish new Hermite-Hadamard Type inequalities for functions whose first derivative in absolute value are preinvex. Further, we give some application of our obtained results to some special means of real numbers. Moreover, we discuss several special cases of the results obtained in this paper.
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    Milne-type inequalities for co-ordinated convex functions
    (Univ Nis, Fac Sci Math, 2024) Shehzadi, Asia; Budak, Huseyin; Haider, Wali; Chen, Haibo
    In this research, our objective is to formulate a unique identity for Milne-type inequalities involving for functions of two variables having convexity on co-ordinates over [mu, v] x [omega, kappa]. By employing this identity, we establish some new inequalities of the Milne-type for co-ordinated convex functions. Furthermore, the propose identity strengthens the theoretical basis of mathematical inequalities showcasing its significance in various fields.
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    Milne-type inequalities for third differentiable and h-convex functions
    (Springer, 2025) Benaissa, Bouharket; Budak, Huseyin
    This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.
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    New approaches to corrected Euler-Maclaurin-type inequalities involving Riemann-Liouville fractional integrals for different function classes
    (Springer, 2025) Kara, Hasan; Hezenci, Fatih; Munir, Arslan; Budak, Huseyin
    This paper investigates several Corrected Euler-Maclaurin-type inequalities for different function classes using Riemann-Liouville fractional integrals. The results, which are derived from special cases of theorems and illustrative examples, are subsequently presented. Furthermore, the authors have developed fractional Corrected Euler-Maclaurin-type inequalities for bounded functions. In addition, the research has acquired fractional Corrected Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, the study concludes with the derivation of fractional Corrected Euler-Maclaurin-type inequalities for functions of bounded variation.
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    NEW EXTENSIONS OF THE HERMITE-HADAMARD INEQUALITIES BASED ON ψ-HILFER FRACTIONAL INTEGRALS
    (Korean Soc Mathematical Education, 2024) Budak, Huseyin; Bas, Umut; Kara, Hasan; Samei, Mohammad Esmael
    This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for 95-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite-Hadamard inequalities via 95-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.
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    NEW EXTENSIONS VERSION OF HERMITE-HADAMARD TYPE INEQUALITIES BY MEANS OF CONFORMABLE FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2024) Bas, Umut; Budak, Huseyin; Kara, Hasan
    In the current investigation, we acquire the upper and lower bounds for inequalities of midpoint-type and trapezoid-type involving conformable fractional integral operators with the help of the mappings whose second derivatives are bounded. We support the established inequalities with examples. Moreover, we use graphs to demonstrate the correctness of the given examples. What's more, we prove the Hermite-Hadamard inequality, which includes conformable fractional integrals, with the aid of condition f ' (a + b t) f ' (t) >= 0, t is an element of a, a+b than the convexity of function.