2-point left Radau-type inequalities via s-convexity

• Autorzy: Meftah Badreddine , Lakhdari Abdelghani , Saleh Wedad

Identyfikatory

DOI

10.1515/jaa-2023-0014

• Języki publikacji: EN

Abstrakty

EN

Convexity is a fundamental concept in analysis. Over the past few decades, many significant error bounds have been established for various quadrature rules using different types of convexity. This paper focuses on the Gauss-Radau quadrature formula. Initially, we introduce a novel identity related to 2-point left Radautype rule. Next, we derive several integral inequalities for functions whose first derivatives are s-convex in the second sense. Finally, we present applications to special means to demonstrate the effectiveness of our results.

Słowa kluczowe

EN

2-point left Radau-type inequalities; s-convex functions; Hölder inequality; power mean inequality

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 341--346
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Meftah Badreddine

• Department of Mathematics, 8 May 1945 University, Geulma, Algeria

• https://orcid.org/0000-0002-0156-7864

autor

Lakhdari Abdelghani

• Department CPST, National Higher School of Technology and Engineering, Annaba, Algeria

• https://orcid.org/0000-0003-2943-2678

autor

Saleh Wedad

• Department of Mathematics, Taibah University, Al-Medina, Saudi Arabia

• https://orcid.org/0000-0003-0600-2624

Bibliografia

• [1] D. C. Benchettah, A. Lakhdari and B. Meftah, Refinement of the general form of the two-point quadrature formulas via convexity, J. Appl. Math. Stat. Inform. 19 (2023), 93-101.
• [2] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) (N. S.) 23(37) (1978), 13-20.
• [3] B. Meftah, A. Lakhdari and D. C. Benchettah, Some new Hermite-Hadamard type integral inequalities for twice differentiable s-convex functions, Comput. Math. Model. 33 (2022), no. 3, 330-353.
• [4] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Eng. 187, Academic, Boston, 1992.
• [5] R. Radau, Etude sur les formules d’approximation qui servent à calculer la valeur numérique d’une intégrale définie, J. Math. Pures Appl. 6 (1880), 283-336.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).