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In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (\alpha ,\beta ,\gamma )$-order and lower $(\alpha ,\beta ,\gamma )$-type, we obtain some growth and oscillation properties of solutions of such equations which improve and extend some recently results of the author and Biswas \cite{b8}., Comment: 22 pages. arXiv admin note: text overlap with arXiv:2308.04208

The main aim of this paper is to study the growth of solutions of higher order linear differential equations using the concepts of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results which improve and generalize some previous results of Kinnunen \cite{13}, Long et al. \cite{L} as well as Bela\"{\i}di \cite{b3}, \cite{b5}., Comment: 21 pages

In this paper, we will give estimates for the logarithmic derivative $ \left\vert \frac{f^{\left( k\right) }\left( z\right) }{f\left( z\right) } \right\vert $ where $f$ is a meromorphic function in a region of the form $ D\left( 0,R\right) =\left\{ z\in \mathbb{C} :0<\left\vert z\right\vert

In this paper we affirm Br\"{u}ck conjecture provided $f$ is of hyper-order less than one by studying the infinite hyper-order of solutions of a complex differential equation.