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Quantitative $m$-exponential convexity and certified bounds for managed traffic link cost models | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 آبان 1405 اصل مقاله (333.71 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.34270.3160 | ||
| نویسنده | ||
| Nemanja Vucicevic Vucicevic* | ||
| Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac | ||
| چکیده | ||
| This paper investigates $m$-exponentially convex functions with respect to $s$. Two new midpoint-type integral inequalities are established using H\"older's inequality and the power-mean inequality. {Structural properties of the associated constants $\Lambda_s$ and $\Omega_s$ are derived; in particular, the strict inequality $3\Omega_s<\Lambda_s$, valid for every $s>0$, shows that, when $q=2$, the power-mean estimate is strictly sharper than the corresponding H\"older estimate.} Sufficient Lipschitz conditions for membership in this class are derived, together with examples showing that it contains functions that are not $m$-convex. A quantitative refinement with an explicit correction term is obtained {; the correction term is proved to be nonnegative, so that the refinement improves the basic $m$-exponential estimate unconditionally and not merely in the reported examples}. {These results are then used as an analytical certification framework for traffic link-cost models, covering both the classical BPR model and a controlled saturating model that may be nonconvex while still belonging to the studied class. In four illustrative cases the correction lowers the baseline $m$-exponential upper bound by $27.6\%$--$30.1\%$, and in a two-link instance a feasible transition flow is constructed whose objective value is within $0.0104\%$ of a certified global optimum. The traffic results are rigorous upper bounds and feasible candidates, not an optimization method or an empirically validated traffic model. | ||
| کلیدواژه‌ها | ||
| $m$-exponential convexity؛ Hermite--Hadamard inequality؛ traffic link cost؛ BPR model؛ system-optimal assignment | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 6 |
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