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4 Journal of Applied Analysis

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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.

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

Meftah Badreddine, Lakhdari Abdelghani, Saleh Wedad

Journal of Applied Analysis

2023

Vol. 29, nr 2

341--346

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.

Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex

Meftah Badreddine

Journal of Applied Analysis

2019

Vol. 25, nr 2

165--171

In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.

Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality

Meftah Badreddine

Journal of Applied Analysis

2019

Vol. 25, nr 1

83--90

In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.