Browsing by Author "LAKHDARI Abdelghan (Co-Auteur)"
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Item Companion of Ostrowski Inequality for Multiplicatively Convex Functions(Sahand Communications in Mathematical Analysis (SCMA), 2024) LAKHDARI Abdelghan (Co-Auteur)The objective of this paper is to examine integral in equalities related to multiplicatively differentiable functions. Ini tially, we establish a novel identity using the two-point Newton Cotes formula for multiplicatively differentiable functions. Using this identity, we derive Companion of Ostrowski’s inequalities for multiplicatively differentiable convex mappings. The work also pro vides the results’ applications.Item Exploring the Companion of Ostrowski’s Inequalities via Local Fractional Integrals(New York Business Global, 2023) LAKHDARI Abdelghan (Co-Auteur)This paper investigates the companion of Ostrowski’s inequality in the framework of fractal sets. First, a new identity related to local fractional integrals is introduced, serving as the foundation for establishing a set of inequalities applicable to functions with generalized s convex and s-concave derivatives. An illustrative example is presented to validate the obtained results, demonstrating their accuracy. Additionally, the paper discusses several practical applica tions, highlighting the significance of the established inequalities. The research presented in this paper contributes to the growing field of studying functions on fractal sets, which has attracted considerable interest from scientists and engineersItem Faulty Detection System Based on SPC and Machine Learning Techniques(Revue d'Intelligence Artificielle, 2022) LAKHDARI Abdelghan (Co-Auteur)Starting from a worrying observation, that companies have difficulties controlling the anomalies of their manufacturing processes, in order to have a better control over them, we have realized a case study on the practical data of the Fertial Complex to analyze the main parameters of the ammonia neutralization by nitric acid process. This article proposes a precise diagnostic of this process to detect dysfunction problems affecting the final product. We start with a general diagnosis of the process using the SPC method, this approach is considered an excellent way to monitor and improve the product quality and provides very useful observations that allowed us to detect the parameters that suffer from problems affecting the quality. After the discovery of the parameters incapable to produce the quality required by the standards, we applies two machine learning technologies dedicated to the type of data of these parameters for detected the anomaly, the first technique called The kernel connectivity-based outlier factor (COF) algorithm consists in recording for each object the degree of being an outlier, the second technique called the Isolation Forest, its principle is to establish a forest to facilitate the calculation and description. The results obtained were compared in order to choose which is the best algorithm to monitor and detect the problems of these parameters, we find that the COF method is more efficient than the isolation forest which leads us to rely on this technology in this kind of process in order to avoid passing a bad quality to the customer in future.Item On Bullen-Type Inequalities for Fractional Integrals with Exponential Kernels(Sahand Communications in Mathematical Analysis (SCMA), 2020) LAKHDARI Abdelghan (Co-Auteur)In this paper, we investigate the Bullen inequality in the context of fractional integrals with exponential kernels. Build ing upon the foundational works in the field, we first introduce a new integral identity. From this identity, we derive several novel Bullen-type inequalities for differentiable convex functions. To vali date our theoretical findings, we provide a numerical example along with graphical representations, demonstrating the accuracy and applicability of our results. The results obtained are not only new for the fractional integrals considered in our study, but as α pproaches 1, we also derive additional novel results for the classical integralItem Parameterized Simpson-like inequalities for differentiable Bounded and Lipschitzian functions with application example from management science(Journal of applied mathematics, statistics and informatics (JAMSI), 2023) LAKHDARI Abdelghan (Co-Auteur)In this paper, based on a given parameterized identity that generates a quadrature rule family similar to Simpson’s second formula, we establish some new Simpson-like type inequalities for functions with bounded as well as Lipchitzian derivatives from which we can deduce the famous 3/8-Simpson’s inequality. The study concludes with an application example from management science.Item Refinement of the general form of the two-point quadrature formulas via convexity(Journal of applied mathematics, statistics and informatics (JAMSI), 2023) LAKHDARI Abdelghan (Co-Auteur)In this paper, we look at the general form of the two-point quadrature formulas, which doesn’t have to be symmetric. Under the convexity constraint of the first derivative, we propose a new scheme that gives the best approximation of the two-point quadrature rules.Item RIGHT-RADAU-TYPE INEQUALITIES FOR MULTIPLICATIVE DIFFERENTIABLE s-CONVEX FUNCTIONS†(Journal of applied mathematics & informatics, 2024) LAKHDARI Abdelghan (Co-Auteur)In this study, a new identity is introduced for multiplicative differentiable functions, forming the foundation for a range of 2-point right Radau-type inequalities applicable to multiplicative s-convex functions. These established results are then showcased through applications that underscore their relevance within the domain of special means.Item Some Weighted Midpoint Type Inequalities For Differentiable log-Convex Functions(Boletim da Sociedade Paranaense de Matemática, 2025) LAKHDARI Abdelghan (Co-Auteur)On the basis of a given integral identity, this paper purports to establish some novel weighted midpoint type inequalities for functions whose first derivatives are log-convex. Traditional integral inequalities, such as Holder’s inequality, are among the integral inequalities that are utilised in proofs, in addition to fundamental definitions and conventional methods of mathematical analysis.Item Strongly Geodesic Log-Preinvex Functions(EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024) LAKHDARI Abdelghan (Co-Auteur)In this article, we delve into the intriguing concept of strongly geodesic log-preinvex functions in Riemannian manifolds. We present essential preliminaries and fundamental results that shed light on this specialized area of study. By examining the properties and implications of these functions, we aim to contribute to the growing body of knowledge in convexity theory within the context of Riemannian manifolds.Item TWO REGULARIZATION METHODS FOR A CLASS OF INVERSE FRACTIONAL PSEUDO–PARABOLIC EQUATIONS WITH INVOLUTION PERTURBATION(Fractional Differential Calculus, 2024) LAKHDARI Abdelghan (Co-Auteur)In this study, we provide a theoretical analysis of an inverse problem governed by a time-fractional pseudo-parabolic equation with involution. The problem is characterized as ill-posed, meaning that the solution (if it exists) does not depend continuously on the measur able data. To address the inherent instability of this problem, we introduce two regularization strategies: the first employs a modified quasi-boundary value method, and the second utilizes a variant of the quasi-reversibility technique. We present convergence results under an a priori bound assumption and propose a practical a posteriori parameter selection rule.