Yazar "Lakhdari, Abdelghani" seçeneğine göre listele

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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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    New insights on fractal-fractional integral inequalities: Hermite-Hadamard and Milne estimates
    (Pergamon-Elsevier Science Ltd, 2025) Lakhdari, Abdelghani; Budak, Huseyin; Mlaiki, Nabil; Meftah, Badreddine; Abdeljawad, Thabet
    This paper investigates fractal-fractional integral inequalities for generalized s-convex functions. We begin by establishing a fractal-fractional Hermite-Hadamard inequality for such functions. In addition, a novel identity is introduced, which serves as the basis for deriving some fractal-fractional Milne-type inequalities for functions whose first-order local fractional derivatives exhibit generalized s-convexity. Subsequently, we provide additional results using the improved generalized H & ouml;lder and power mean inequalities, followed by a numerical example with graphical representations that confirm the accuracy of the obtained results. The study concludes with several applications to demonstrate the practicality and relevance of the proposed inequalities in various settings.