Growth estimates of solutions of linear differential equations with dominant coefficient of lower $(α,β,γ)$-order

Abstract: 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}.