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Research Article | Open Access

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

Praveen Agarwal1, Miguel Vivas-Cortez2 ( ), Yenny Rangel-Oliveros2, Muhammad Aamir Ali3
Department of mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India
Pontificia Universidad Católica del Ecuador, Facultad de Ciencias Naturales y Exactas, Escuela de Ciencias Físicas y Matemáticas, Sede Quito, Ecuador
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
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Abstract

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

Keywords

φ-convex functions-convex functions-φ-convex functions-φb-convex functionOstrowski inequality
CLC number: 26D07, 26D10, 26D15, 26B15, 26B25

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1429-1444
DOI: 10.3934/math.2022084

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Cite this article:
Agarwal P, Vivas-Cortez M, Rangel-Oliveros Y, et al. New Ostrowski type inequalities for generalized s-convex functions with applications to some special means of real numbers and to midpoint formula. AIMS Mathematics, 2022, 7(1): 1429-1444. https://doi.org/10.3934/math.2022084

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Received: 22 April 2021
Accepted: 20 August 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)