In thispaper, we introduce and consider a new problem of finding mu is an element of K(u) such that Au is an element of C, where K: u -> K(u) is a closed convex-valued set in the real Hilbert space H-1, C is closed convex set in the real Hilbert space H-2 respectively and A is linear bounded self-adjoint operator from H-1 and H-2. This problem is called the quasi split feasibility problem. We show that the quasi feasibility problem is equivalent to the fixed point problem and quasi variational inequality. These s alternative equivalent formulations are used to consider the existence of a solution of the quasi split feasibility problem. Some special cases are also considered. Problems considered in this paper may open further research opportunities in these fields.