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Taylor's formula for general quantum calculus | ||
Journal of Mathematical Modeling | ||
مقاله 6، دوره 11، شماره 3، دی 2023، صفحه 491-505 اصل مقاله (173.63 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.22124/jmm.2023.23936.2139 | ||
نویسندگان | ||
Svetlin G. Georgiev1؛ Sanket Tikare* 2 | ||
1Department of Mathematics, Sorbonne University, Paris, France | ||
2Department of Mathematics, Ramniranjan Jhunjhunwala College,\\ Mumbai, Maharashtra 400 086, India | ||
چکیده | ||
Let $I\subseteq\mathbb{R}$ be an interval and $\beta\colon I\to I$ a strictly increasing continuous function with a unique fixed point $s_0\in I$ satisfying $(t-s_0)(\beta(t)-t)\le 0$ for all $t\in I$. Hamza et al. introduced the general quantum difference operator $D_{\beta}$ by $D_{\beta}f(t):=\frac{f(\beta(t))-f(t)}{\beta(t)-t}$ if $t\ne s_0$ and $D_{\beta}f(t):=f'(s_0)$ if $t=s_0$. In this paper, we establish results concerning Taylor's formula associated with $D_{\beta}$. For this, we define two types of monomials and then present our main results. The obtained results are new in the literature and are useful for further research in the field. | ||
کلیدواژهها | ||
Quantum calculus؛ quantum difference operator؛ $\beta$-derivative؛ $\beta$-integral؛ Taylor's formula؛ monomials | ||
آمار تعداد مشاهده مقاله: 299 تعداد دریافت فایل اصل مقاله: 352 |