T. D. NARANG - Department of Mathematics, Guru Nanak Dev University, Amritsar-143001, India. SUMIT CHANDOK - School of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India.
For a subset \(K\) of a metric space \((X, d)\) and \(x \in X\), the set \(P_K(x) = \{y \in K : d(x, y) = d(x;K) \equiv \inf\{d(x, k) : k \in K\}\}\) is called the set of best \(K\) -approximant to \(x\). An element \(g_\circ \in K\) is said to be a best simultaneous approximation of the pair \(y_1, y_2 \in X\) if \[\max\{d(y_1, g_\circ), d(y_2, g_\circ)\} = \inf_{g\in K} \max\{d(y_1, g), d(y_2, g)\}.\] Some results on \(T\)-invariant points for a set of best simultaneous approximation to a pair of points \(y_1, y_2\) in a convex metric space \((X, d)\) have been proved by imposing conditions on \(K\) and the self mapping \(T\) on \(K\) . For self mappings \(T\) and \(S\) on \(K\) , results are also proved on both \(T\)- and \(S\)- invariant points for a set of best simultaneous approximation. The results proved in the paper generalize and extend some of the results of \(P\). Vijayaraju [Indian J. Pure Appl. Math. 24(1993) 21-26]. Some results on best \(K\) -approximant are also deduced.
T. D. NARANG, SUMIT CHANDOK, SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS, Journal of Nonlinear Sciences and Applications, 3 (2010), no. 2, 87-95
NARANG T. D., CHANDOK SUMIT, SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS. J. Nonlinear Sci. Appl. (2010); 3(2):87-95
NARANG , T. D., CHANDOK, SUMIT. "SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS." Journal of Nonlinear Sciences and Applications, 3, no. 2 (2010): 87-95
