Chao Wang, Guangzhou Qin, Ravi P. Agarwal
abstract:
In this paper, we introduce a notion of jump operators along the assigned
direction $\vec{\omega}$ and the corresponding opposite direction $-\vec{\omega}$
on an $n$-dimensional time scale $\Lambda^{n}$, due to which the total increment
of the multivariate function can be represented accurately. Based on it, we
introduce the new notions of directional derivatives and gradient of
multivariate function on time scales and demonstrate their nice geometric
significance. Moreover, some basic results are established which improve and
perfect the previous literature.
Mathematics Subject Classification: 26E70, 34N05
Key words and phrases: Time scale, jump operators along the assigned direction, directional derivative, gradient, partial derivative