Convex Functions on Discrete Time Domains
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 225-233
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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.
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
@article{10_4153_CMB_2015_065_6,
author = {At{\i}c{\i}, Ferhan M. and Yald{\i}z, Hatice},
title = {Convex {Functions} on {Discrete} {Time} {Domains}},
journal = {Canadian mathematical bulletin},
pages = {225--233},
year = {2016},
volume = {59},
number = {2},
doi = {10.4153/CMB-2015-065-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-065-6/}
}
TY - JOUR AU - Atıcı, Ferhan M. AU - Yaldız, Hatice TI - Convex Functions on Discrete Time Domains JO - Canadian mathematical bulletin PY - 2016 SP - 225 EP - 233 VL - 59 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-065-6/ DO - 10.4153/CMB-2015-065-6 ID - 10_4153_CMB_2015_065_6 ER -
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