TY - JOUR
ID - 4276
TI - Diamond-$\phi_h$ dynamics on time scales with an application to economics
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Opeyemi, Fagbemigun
AU - Alao, Mogbademu
AU - Olajiire, Olaleru
AD - Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Nigeria
AD - Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria
Y1 - 2020
PY - 2020
VL - 11
IS - 1
SP - 277
EP - 290
KW - time scales
KW - $phi_{h}$-concave
KW - diamond-$phi_{h}$
KW - Hermite-Hadamard
KW - dynamic model
DO - 10.22075/ijnaa.2020.19155.2059
N2 - Conventional dynamic models in economics are usually expressed in discrete or continuous time. A new modelling technique-time scales calculus-unifies both of these approaches into a general framework. We present and construct a dynamic optimization problem from economics in which the utility function is $\phi_{h}$-concave and the value function and constraints are on different time scales. The calculus of variations and optimal control are employed, with the aid of the newly introduced diamond-$\phi_{h}$ dynamic calculus by the authors [12] on time scales, to obtain a solution. The Hermite-Hadamard inequality with the diamond-$\phi_{h}$ dynamic integral follows a proof of the new model. The new diamond-$\phi_{h}$ time scale model unifies various related existing models involving general and more complex time domains.
UR - https://ijnaa.semnan.ac.ir/article_4276.html
L1 - https://ijnaa.semnan.ac.ir/article_4276_d858c058f79d957edc47ab3d979b2cd4.pdf
ER -