Browsing by Author "LAKHDARI Abdelghani (Co-Auteur)"

Now showing 1 - 8 of 8
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    On fractional biparameterized Newton-type inequalities
    (Journal of Inequalities and Applications, 2023) LAKHDARI Abdelghani (Co-Auteur)
    In this work, we present a novel biparameterized identity that yields a family of one-, two-, three-, and four-point Newton-type formulas. Subsequently, we establish some new Newton-type inequalities for functions whose first derivatives are α-convex. The investigation is concluded with numerical examples accompanied by graphical representations to substantiate the accuracy of the obtained results.
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    On multiparametrized integral inequalities via generalized 𝛼-convexity on fractal set
    (Mathematical Methods in the Applied Sciences, 2024) LAKHDARI Abdelghani (Co-Auteur)
    This article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized 𝛼-convex functions. It introduces a novel extension of the Hermite-Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings.
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    On parameterized inequalities for fractional multiplicative integrals
    (Demonstratio Mathematica, 2024) LAKHDARI Abdelghani (Co-Auteur)
    In this article, we present a one-parameter fractional multiplicative integral identity and use it to derive a set of inequalities for multiplicatively s-convex mappings. These inequalities include new discoveries and improvements upon some well-known results. Finally, we provide an illustrative example with graphical representations, along with some applications to special means of real numbers within the domain of multiplicative calculus.
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    On the multiparameterized fractional multiplicative integral inequalities
    (Journal of Inequalities and Applications, 2024-04) LAKHDARI Abdelghani (Co-Auteur)
    We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.
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    Parametrized multiplicative integral inequalities
    (Advances in Continuous and Discrete Models, 2024) LAKHDARI Abdelghani (Co-Auteur)
    In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers’ comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations. Finally, we demonstrate the applicability of our results to special means of real numbers within the realm of multiplicative calculus.
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    Some Error Bounds for 2-Point Right Radau Formula in the Setting of Fractional Calculus via s-Convexity
    (Journal of Mathematics, 2024) LAKHDARI Abdelghani (Co-Auteur)
    In this paper, we present a new approach to construct fractional 2-point right Radau type integral inequalities using a novel identity, for functions with s-convex 1rst derivatives in the second sense via Riemann–Liouville fractional integral operators. We then demonstrate the accuracy of our results through a 2D example, as well as practical applications of the integral inequalities to quadrature formulas and special means such as arithmetic and p-logarithmic means.
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    Some New Fractal Milne-Type Integral Inequalities via Generalized Convexity with Applications
    (Fractal and Fractional, 2023) LAKHDARI Abdelghani (Co-Auteur)
    This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper’s findings represent a significant improvement over previously published results. The paper’s ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field.
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    Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized (E, h)-Convexity
    (Mathematics, 2023) LAKHDARI Abdelghani (Co-Auteur)
    In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite– Hadamard-type inequality using generalized (E, h)-convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. In terms of applications, we provide some new generalized trapezoid-type inequalities for generalized (E, h)-convex functions. Finally, some special cases are deduced for different values of δ, E, and h.