Correction to "New issues and results in nonlinear systems stability"
Abstract
In paper "New issues and results in nonlinear systems stability" by Itzhak Barkana, which appeared in MESA (MATHEMATICS IN ENGINEERING, SCIENCE AND AEROSPACE), Vol. 11, No. 3, pp. 671-684, 2020, a typo fell that might confuse the reader.
At the end of section 5.2, maybe under the influence of the previous example of section 5.1, an erroneous division by t appears. Therefore, instead of
$\dot{f}_k(t)=\frac{df_k(t)}{dt}=\mathop {\lim }\limits_{h \to 0 }(\mathop {\lim }\limits_{t \to \infty }{(\frac{f_k(t+h)-f_k(t)}{h}))}
=\mathop {\lim }\limits_{h \to 0 }(\mathop {\lim }\limits_{t \to \infty }{(\frac{\frac{sin((t+h)e^{-(t+h)^{2k}sin^2(t+h)})}{t+h}-\frac{sin(t)e^{-t^{2k}sin^2(t)}}{t}}{h})})$
should be
$\dot{f}_k(t)=\frac{df_k(t)}{dt}=\mathop {\lim }\limits_{h \to 0 }(\mathop {\lim }\limits_{t \to \infty }{(\frac{f_k(t+h)-f_k(t)}{h}))}
=\mathop {\lim }\limits_{h \to 0 }(\mathop {\lim }\limits_{t \to \infty }{(\frac{sin(t+h)e^{-(t+h)^{2k}sin^2(t+h)}-sin(t)e^{-t^{2k}sin^2(t)}}{h}}))$
All the rest remain the same.