Strongly Convex Functions of Higher Order Involving Bifunction

Strongly Convex Functions of Higher Order Involving Bifunction

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...

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Veröffentlicht in:Mathematics (Basel) 2019-11, Vol.7 (11), p.1028
Hauptverfasser: Mohsen, Bandar B., Noor, Muhammad Aslam, Noor, Khalida Inayat, Postolache, Mihai
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Convex analysis
convex function
Equilibrium
Mathematics
monotone operator
strongly convex function
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7111028