Geodesic
Convex Functions on Discrete Time Domains
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 225-233

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we introduce the definition of a convex real valued function $f$ defined on the set of integers, $\mathbb{Z}$ . We prove that $f$ is convex on $\mathbb{Z}$ if and only if ${{\Delta }^{2}}f\,\ge \,0$ on $\mathbb{Z}$ . As a first application of this new concept, we state and prove discrete Hermite–Hadamard inequality using the basics of discrete calculus (i.e., the calculus on $\mathbb{Z}$ ). Second, we state and prove the discrete fractional Hermite–Hadamard inequality using the basics of discrete fractional calculus. We close the paper by defining the convexity of a real valued function on any time scale.
DOI : 10.4153/CMB-2015-065-6
Mots-clés : 26B25, 26A33, 39A12, 39A70, 26E70, 26D07, 26D10, 26D15, discrete calculus, discrete fractional calculus, convex functions, discrete Hermite–Hadamard inequality 
Atıcı, Ferhan M.; Yaldız, Hatice. Convex Functions on Discrete Time Domains. Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 225-233. doi: 10.4153/CMB-2015-065-6
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