No CrossRef data available.
Published online by Cambridge University Press: 07 July 2022
In this work, we consider the first-order difference equation with general argument
is a sequence of non-negative real numbers, $(\tau (n))$
is a sequence of integers such that $\tau (n)< n$
for$\ n\in \mathbf {N},\,$
and$\ \lim _{n\rightarrow \infty }\tau (n)=\infty.$
Under the assumption that the deviating argument is not necessarily monotone, we obtain some new oscillation conditions and improve the all known results for the above equation in the literature, involving only upper and only lower limit conditions. Two examples illustrating the results are also given.