(untitled) (Analysis in Theory and Applications, 2012)
For a subset K of a metric space (X,d) and x ∈ X,P_K(x)={yK : d(x, y)= d(x, K) ≡inf{d(x, k) : k K}} is called the set of best K-approximant to x. An element g◦K is said to be a best simultaneous approximation of the pair y_1, y_2 X if max{d(y_1, g◦), d(y_2, g◦)}= _gK max{d(y_1, g), d(y_2, g)}. In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T- and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas[1], S. Chandok and T. D. Narang[2], T. D. Narang and S. Chandok[11], S. A. Sahab, M. S. Khan and S. Sessa[14], P. Vijayaraju[20] and P. Vijayaraju and M. Marudai[21].