New Ostrowski type inequalities for generalized $ s $-convex functions with applications to some special means of real numbers and to midpoint formula

Praveen Agarwal; Miguel Vivas-Cortez; Yenny Rangel-Oliveros; Muhammad Aamir Ali; Praveen Agarwal; Miguel Vivas-Cortez; Yenny Rangel-Oliveros; Muhammad Aamir Ali

doi:10.3934/math.2022084

AIMS Mathematics

2022, Volume 7, Issue 1: 1429-1444. doi: 10.3934/math.2022084

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New Ostrowski type inequalities for generalized $ s $-convex functions with applications to some special means of real numbers and to midpoint formula

1.
Department of mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India
2.
Pontificia Universidad Católica del Ecuador, Facultad de Ciencias Naturales y Exactas, Escuela de Ciencias Físicas y Matemáticas, Sede Quito, Ecuador
3.
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

Received: 22 April 2021 Accepted: 20 August 2021 Published: 26 October 2021
MSC : 26D07, 26D10, 26D15, 26B15, 26B25

In this paper we establish new Ostrowski type inequalities related to the notion s-$ \varphi $-convex functions (see ^[37]), were $ f\in C^n([a, b]) $ with $ f^{(n)}\in L([a, b]) $ and we give some applications to some special means, the midpoint formula and some examples for the case $ n = 2 $.
- $ \varphi $-convex function,
- $ s $-convex function,
- s-$ \varphi $-convex function,
- s-$ \varphi_b $-convex function,
- Ostrowski inequality
Citation: Praveen Agarwal, Miguel Vivas-Cortez, Yenny Rangel-Oliveros, Muhammad Aamir Ali. New Ostrowski type inequalities for generalized $ s $-convex functions with applications to some special means of real numbers and to midpoint formula[J]. AIMS Mathematics, 2022, 7(1): 1429-1444. doi: 10.3934/math.2022084

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Abstract

In this paper we establish new Ostrowski type inequalities related to the notion s-$ \varphi $-convex functions (see ^[37]), were $ f\in C^n([a, b]) $ with $ f^{(n)}\in L([a, b]) $ and we give some applications to some special means, the midpoint formula and some examples for the case $ n = 2 $.

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