eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2016-08-31 4 4 87 91 10.12691/tjant-4-4-1 TJANT2016441 article Valdete Rexh?beqaj Hamiti valdete_r@hotmail.com 1 Shqipe Lohaj 1 Qefsere Gjonbalaj 1 Faculty of Electrical and Computer Engineering, University of Prishtina, Prishtin?, Kosova Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class of operators: k-quasi class Q* operators. An operator T is said to be k-quasi class Q* if it satisfies for all xH, where k is a natural number. We prove the basic properties of this class of operators. http://pubs.sciepub.com/tjant/4/4/1/tjant-4-4-1.pdf k-quasi class Q^* quasi class Q^* k-quasi -*- paranormal operators quasi -*- paranormal operators