Published Paper Details:

Given a point g and a set M in a Normed linear space, a point of M of minimum distance from g is called a best approximation and the problem of determining such a point is called best approximation problem. Our Main aims are then to investigate important example of such problems, with particular regards of - (1) The existence of best approximation. (2) The uniqueness of best approximation. (3) The characterization of best approximation. (4) The construction of method for determining best approximation. It is clear that the existence of a solution to approximation problems requires certain additional conditions to be satisfied. We will not deal with this aspect of the problem to any great extent, but will be concentrated rather on the treatment of problems for which the normed linear space S, set M and point g are assumed given motivation for the use of any particular norm will however, be given where appropriate. The task of characterizing best approximations is that of deriving potentially useful conditions which a best approximation must satisfy, and which, if satisfied guarantee that a particular approximation is indeed a best approximation. The importance of approximation problems have solution which is characterized by conditions which can be used directly as a means of actually calculating such best approximations. The construction of this solution by their means forms an important part of this paper and results are included in algorithms.