In thispaper, we introduce and consider a new problem of finding u2 K(u) such that Au2 C, where K : u! K(u) is a closed convex-valued set in the real Hilbert space H1, C is closed convex set in the real Hilbert space H2 respectively and A is linear bounded self-adjoint operator from H1 and H2. This problem is called the quasi split feasibility problem. We show that the qu asi feasibility problem is equivalent to the fixed point problem and quasi variational ine quality. These s alternative equivalent formulations are used to consider the existence of a solution of the quasi split feasibility problem. So me special cases are also considered. Problems considered in this paper may open further research opportunities in these fields.