Geodesic
SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS
NARANG , T. D. 1 ; CHANDOK, SUMIT2
1 Department of Mathematics, Guru Nanak Dev University, Amritsar-143001, India
2 School of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India
Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 87-95.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.003.02.02
Classification : 47H10, 54H25
Keywords: Best approximation, fixed point, nonexpansive, R-weakly commuting, R-subweakly commuting, asymptotically nonexpansive and uniformly asymptotically regular maps.

NARANG , T. D.  1 ; CHANDOK, SUMIT 2

1 Department of Mathematics, Guru Nanak Dev University, Amritsar-143001, India
2 School of Mathematics and Computer Applications, Thapar University, Patiala- 147004, India 
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NARANG , T. D. ; CHANDOK, SUMIT. SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 2, p. 87-95. doi : 10.22436/jnsa.003.02.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.02.02/

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