Belabbaci Chafika2021-09-052021-09-052021http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/25307In this paper, we study the spectral radius of some S-essential spectra of a bounded linear operator defined on a Banach space. More precisely, via the concept of measure of noncompactness, we show that for any two bounded linear operators T and S with S non zero and non compact operator the spectral radius of the S-Gustafson, S-Weidmann, S-Kato and S-Wolf essential spectra are given by the following inequalities (T) (S) re;S(T) (T) (S) ; (1) where (:) stands for the Kuratowski measure of noncompactness and (:) is defined in [11]. In the particular case when the index of the operator S is equal to zero, we prove the last inequalities for the spectral radius of the S-Schechter essential spectrum. Also, we prove that the spectral radius of the S-Jeribi essential spectrum satisfies inequalities (2) when the Banach space X has no reflexive infinite dimensional subspace and the index of the operator S is equal to zero (the S-Jeribi essential spectrum, introduced in [7] as a generalisation of the Jeribi essential spectrum).Article