Yazar "Chen, Haibo" seçeneğine göre listele

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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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    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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    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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    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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    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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    On new versions of Milne-type inequalities based on tempered fractional integrals
    (World Scientific Publ Co Pte Ltd, 2025) Shehzadi, Asia; Budak, Huseyin; Haider, Wali; Hezenci, Fatih; Chen, Haibo
    This investigation reveals significant identity related to the Milne-type inequalities. Utilizing this identity, we derive Milne-type inequalities by incorporating differentiable convex mappings, including tempered fractional integrals. Our strategy involves delving into notable functional categories such as convex, bounded, Lipschitzian, and functions with bounded variation. What's more, new findings are achieved through special choices.