Taylor's formula for general quantum calculus
عنوان مقاله: Taylor's formula for general quantum calculus
شناسه ملی مقاله: JR_JMMO-11-3_006
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_JMMO-11-3_006
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Svetlin Georgiev - Department of Mathematics, Sorbonne University, Paris, France
Sanket Tikare - Department of Mathematics, Ramniranjan Jhunjhunwala College,\\ Mumbai, Maharashtra ۴۰۰ ۰۸۶, India
خلاصه مقاله:
Svetlin Georgiev - Department of Mathematics, Sorbonne University, Paris, France
Sanket Tikare - Department of Mathematics, Ramniranjan Jhunjhunwala College,\\ Mumbai, Maharashtra ۴۰۰ ۰۸۶, India
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_۰\in I satisfying (t-s_۰)(\beta(t)-t)\le ۰ 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_۰ and D_{\beta}f(t):=f'(s_۰) if t=s_۰. 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.
کلمات کلیدی: Quantum calculus, quantum difference operator, \beta-derivative, \beta-integral, Taylor's formula, monomials
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1995544/