On the Sum of Simultaneously f-Proximinal Subspaces and Quotient Spaces

In this paper we introduce the concept of f -simultaneous approximation in Banach spaces and prove some results concerning simultaneous f-approximation of the sum of two subspaces G and F of a Banach space X, where f is an increasing continuous non-negative real valued function defined on [0, ∞). Some other results are also presented. Mathematics Subject Classification: Primary 41A50, Secondary 41A28