Continuous Selections of the Set-Valued Metric Generalized Inverse in 2-Strictly Convex Banach Spaces

In this paper, we prove that if X is an almost convex and 2-strictly convex space, linear operator T:X -> Y is bounded, N(T) is an approximative compact Chebyshev subspace of X and R(T) is a 3-Chebyshev hyperplane, then there exists a homogeneous selection T-sigma of T- partial differential such that continuous points of T-sigma and T- partial differential are dense on Y.