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Article

Better Approaches for n-Times Differentiable Convex Functions

by
Praveen Agarwal
1,2,3,4,†,
Mahir Kadakal
5,†,
İmdat İşcan
5,† and
Yu-Ming Chu
6,7,*,†
1
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India
2
International Center for Basic and Applied Sciences, Jaipur 302029, India
3
Department of Mathematics, Harish-Chandra Research Institute, Allahabad 211019, India
4
Department of Mathematics, Netaji Subhas University of Technology Dwarka Sector-3, Dwarka, Delhi 110078, India
5
Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun 28200, Turkey
6
Department of Mathematics, Huzhou University, Huzhou 313000, China
7
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2020, 8(6), 950; https://doi.org/10.3390/math8060950
Submission received: 25 April 2020 / Revised: 25 May 2020 / Accepted: 27 May 2020 / Published: 10 June 2020
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
Versions Notes

Abstract

In this work, by using an integral identity together with the Hölder–İşcan inequality we establish several new inequalities for n-times differentiable convex and concave mappings. Furthermore, various applications for some special means as arithmetic, geometric, and logarithmic are given.
Keywords: convex function; Hölder–İşcan integral inequality convex function; Hölder–İşcan integral inequality

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MDPI and ACS Style

Agarwal, P.; Kadakal, M.; İşcan, İ.; Chu, Y.-M. Better Approaches for n-Times Differentiable Convex Functions. Mathematics 2020, 8, 950. https://doi.org/10.3390/math8060950

AMA Style

Agarwal P, Kadakal M, İşcan İ, Chu Y-M. Better Approaches for n-Times Differentiable Convex Functions. Mathematics. 2020; 8(6):950. https://doi.org/10.3390/math8060950

Chicago/Turabian Style

Agarwal, Praveen, Mahir Kadakal, İmdat İşcan, and Yu-Ming Chu. 2020. "Better Approaches for n-Times Differentiable Convex Functions" Mathematics 8, no. 6: 950. https://doi.org/10.3390/math8060950

APA Style

Agarwal, P., Kadakal, M., İşcan, İ., & Chu, Y.-M. (2020). Better Approaches for n-Times Differentiable Convex Functions. Mathematics, 8(6), 950. https://doi.org/10.3390/math8060950

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