Hermite-Hadamard Type Inequalities via the Montgomery Identity

Authors

  • Muhammad Adil Khan College of Science, Hunan City University, Yiyang 413000, China; Department of Mathematics, University of Peshawar, Peshawar 25000
  • Yousaf Khurshid Department of Mathematics, University of Peshawar, Peshawar 25000
  • Yu-Ming Chu Department of Mathematics, Huzhou University, Huzhou 313000

DOI:

https://doi.org/10.26713/cma.v10i1.1178

Keywords:

Montgomery identity, Convex function, Hermite-Hadamard inequality, Means

Abstract

The main aim of this manuscript is to prove the result for Hermite-Hadamard types inequalities and to strengthen our results by giving applications for means. The proof of the result is based on the Montgomery identity. We use the Montgomery identity to establish a new identity regarding the Hermite-Hadamard inequality. Based on this identity with a class of convex and monotone functions and Jensen's inequality, we obtain various results for the inequality. At the end, we also present applications for special bivariate means.

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Published

31-03-2019
CITATION

How to Cite

Khan, M. A., Khurshid, Y., & Chu, Y.-M. (2019). Hermite-Hadamard Type Inequalities via the Montgomery Identity. Communications in Mathematics and Applications, 10(1), 85–97. https://doi.org/10.26713/cma.v10i1.1178

Issue

Vol. 10 No. 1 (2019)

Section

Research Article

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