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Diamond-$\phi_h$ dynamics on time scales with an application to economics | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 22، دوره 11، شماره 1، تیر 2020، صفحه 277-290 اصل مقاله (401.45 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.19155.2059 | ||
| نویسندگان | ||
| Fagbemigun Opeyemi* 1؛ Mogbademu Alao2؛ Olaleru Olajiire2 | ||
| 1Department of Mathematics, Faculty of Science, University of Lagos, Akoka, Nigeria | ||
| 2Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria | ||
| تاریخ دریافت: 01 آذر 1398، تاریخ بازنگری: 18 دی 1398، تاریخ پذیرش: 13 بهمن 1398 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Time scales؛ $\phi_{h}$-concave؛ diamond-$\phi_{h}$؛ Hermite-Hadamard؛ dynamic model | ||
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