Volume 28, Issue 1
Common Fixed Points with Applications to Best Simultaneous Approximations

Sumit Chandok and T. D. Narang


Anal. Theory Appl., 28 (2012), pp. 1-12

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  • Abstract

For a subset K of a metric space (X,d) and x ∈ X,P_K(x)={y∈K : 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 simultaneousapproximation of the pair y1,y2 ∈ X ifmaxd(y1, g◦), d(y2, g◦)}= inf_{g∈K} max{d(y_1, g), d(y_2, g)}. In this paper, some results on the existence of common fixed points for Banach operatorpairs in the framework of convex metric spaces have been proved. For self mappings Tand S on K, results are proved on both T- and S- invariant points for a set of best simultaneousapproximation. Some results on best K-approximant are also deduced. The resultsproved 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].

  • History

Published online: 2012-03

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