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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

2-point right Radau inequalities for differentiable s-convex functions

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pp. 1243–1255Vol. 27Issue 6September 2024DOI: 10.47974/JIM-1741XML
Received:
08 Feb 2023
Published Online:
30 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1741
Pages:
1243–1255

Abstract

Convexity is one of the fundamental principles of analysis. In the last decades, many important inequalities are established for different classes of convex functions. In this paper, we propose to study a 2-point right Radau type integral inequalities for functions whose first derivatives are s-convex in the second sense. The cases where the first derivatives are bounded as well as Hölderian are also discussed. Applications to quadrature formulas and special means are provided.

Keywords

Subject Classifications

(2010) 26D1026D1526A51

References

[1] N. Azzouza and B. Meftah, Some weighted integral inequalities for differentiable beta-convex functions. J. Interdiscip. Math. 25, no. 2, 373-393 (2022).
[2] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen. (German) Publ. Inst. Math. (Beograd) (N.S.) 23 (37), 13-20 (1978).
[3] M. Çakmak, Refinements of bullen-type inequalities for s-convex functions via Riemann-Liouville fractional integrals involving Gauss hypergeometric function. J. Interdiscip. Math. 22, no. 6, 975-989 (2019).
[4] B. Meftah, M. Merad and A. Souahi, Fractional Ostrowski type inequalities for functions whose mixed derivatives are prequasiinvex functions. J. Interdiscip. Math. 22, no. 5-6, 1-17 (2019).
[5] Meftah and K. Mekalfa, Some weighted trapezoidal inequalities for differentiable log-convex functions. J. Interdiscip. Math. 24, no. 3, 505-517 (2021).
[6] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA (1992).
[7] R. Radau, Etude sur les formules d’approximation qui servent à calculer la valeur numérique d’une intégrale définie. J. Math. Pures et Appl., 6, pp. 283-336 (1880).
[8] B.-Y. Xi, S.-P. Bai and F. Qi, On integral inequalities of the Hermite-Hadamard type for co-ordinated (α1, m1) -(α2, m2) -convex functions. J. Interdiscip. Math. 21, no. 7-8, 1505-1518 (2018).

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