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Open AccessArticle

Strongly Convex Functions of Higher Order Involving Bifunction

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Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
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Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan
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Center for General Education, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1028; https://doi.org/10.3390/math7111028
Received: 28 September 2019 / Revised: 24 October 2019 / Accepted: 26 October 2019 / Published: 1 November 2019
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. View Full-Text
Keywords: convex function; monotone operator; strongly convex function convex function; monotone operator; strongly convex function
MDPI and ACS Style

Mohsen, B.B.; Noor, M.A.; Noor, K.I.; Postolache, M. Strongly Convex Functions of Higher Order Involving Bifunction. Mathematics 2019, 7, 1028.

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