Strongly Convex Functions of Higher Order Involving Bifunction

Bandar B. Mohsen, Muhammad Aslam Noor, Khalida Inayat Noor and Mihai Postolache
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Bandar B. Mohsen: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
Muhammad Aslam Noor: Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
Khalida Inayat Noor: Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
Mihai Postolache: Center for General Education, China Medical University, Taichung 40402, Taiwan

Mathematics, 2019, vol. 7, issue 11, 1-12

Abstract: Some new concepts of the higher order strongly convex functions involving an arbitrary bifuction are considered in this paper. Some properties of the higher order strongly convex functions are investigated under suitable conditions. Some important special cases are discussed. The parallelogram laws for Banach spaces are obtained as applications of higher order strongly affine convex functions as novel applications. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

Keywords: convex function; monotone operator; strongly convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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