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Weighted Simpson-like type inequalities for quasi-convex functions

Ayed Hamida, Meftah Badreddine

Journal of Applied Analysis

2023

Vol. 29, nr 2

313--322

In this paper, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 (2018), Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper.

On certain subclasses of close-to-convex and

Wang Z-G., Jiang Y-P.

Journal of Mathematics and Applications

2007

Vol. 29

167-179

In the present paper, the authors introduce two new subclasses S(sup k) (sub sc) (γ, α β) of close-to-convex functions and C(sup k) (sub sc) (γ, α β) of quasi-convex functions with respect to 2k-symmetric conjugate points. The inclusion and subordination relationships, convolution conditions for these classes are provided. The coefficient inequalities, integral representations and sufficient conditions for functions belonging to these classes are also provided.

Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions

Cerone P., Dragomir S.

Demonstratio Mathematica

2004

Vol. 37, nr 2

299--308

Ostrowski type inequalities for absolutely continuous functions whose derivatives satisfy certain convexity assumptions are pointed out.