A Carleman-Knopp Type Inequality for Pseudo-Integral | ||
| Mathematics Interdisciplinary Research | ||
| دوره 10، شماره 3، آذر 2025، صفحه 315-335 اصل مقاله (674.49 K) | ||
| نوع مقاله: Original Scientific Paper | ||
| شناسه دیجیتال (DOI): 10.22052/mir.2025.257212.1527 | ||
| نویسندگان | ||
| Mohammadreza Yasamian؛ Mohsen Jaddi* | ||
| Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran | ||
| چکیده | ||
| Pseudo-analysis has applications in several fields, including game theory and optimization problems. Pseudo-analysis is a generalized form of ordinary classical analysis that has two main operations. In fact, these two operations, which are called pseudo-multiplication $\otimes$ and pseudo-addition $\oplus$, are the basis of the formation of a semi-ring on the interval [c,d] of $ [-\infty,\infty]$. The pseudo-operations $\otimes$ and $\oplus$ on [c,d] produce three types of semi-ring. First, the semi-ring $([c,d],\sup,\otimes)$ or $([c,d],\inf,\otimes)$ in which $\otimes$ is generated, the second, a semi-ring where $\otimes$ and $\oplus$ are defined by the continuous and strictly monotone function $\psi$, the third, a semi-ring in which both pseudo-operations $\otimes$ and $\oplus$ are idempotent. In this article, we intend to state and prove some of the most recent generalizations of Carleman-Knopp's type inequalities via pseudo-integrals. | ||
| کلیدواژهها | ||
| Pseudo-operation؛ Pseudo-integral؛ Pseudo-logarithm | ||
| مراجع | ||
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