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The concept of coordinate strongly convex functions and related inequalities

  • Muhammad Adil Khan
  • Syed Zaheer Ullah
  • Yu-Ming Chu
Original Paper
  • 21 Downloads

Abstract

In this paper, we introduce a new class of functions known as coordinate strongly convex functions. We discuss the relation between strongly convex functions and coordinate strongly convex functions. Also, we present some natural properties of coordinate strongly convex functions. We present Slater’s, Jensen’s and converse of the Jensen inequalities in discrete as well as integral versions for coordinate strongly convex functions. Furthermore, we present Hermite–Hadamard’s type inequalities for coordinate strongly convex functions.

Keywords

Coordinate strongly convex function Jensen’s inequality Slater’s inequality 

Mathematics Subject Classification

Primary 26D15 26A51 Secondary 39B62 

Notes

Acknowledgements

The research was supported by the Natural Science Foundation of China (Grant Nos. 61373169, 11701176, 11601485 ) and the Science and Technology Research Program of Zhejiang Educational Committee (Grant no. Y201635325). The third author Yu-Ming Chu is the corresponding author of the article. The authors would like to express their sincere thanks to anonymous referees for their valuable suggestions and comments which helped the authors to improve this article substantially.

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Copyright information

© The Royal Academy of Sciences, Madrid 2018

Authors and Affiliations

  1. 1.College of ScienceHunan City UniversityYiyangChina
  2. 2.Department of MathematicsUniversity of PeshawarPeshawarPakistan
  3. 3.Department of MathematicsHuzhou UniversityHuzhouChina

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