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

Sumit Chandok & T. D. Narang

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

Published online: 2012-03

Preview Full PDF 352 827
Export citation
  • 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].

  • Keywords

Banach operator pair best approximation demicompact fixed point star-shaped nonexpansive asymptotically nonexpansive and uniformly asymptotically regular maps

  • AMS Subject Headings

41A50 41A60 41A65 47H10 54H25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{ATA-28-1, author = {Sumit Chandok and T. D. Narang}, title = {Common Fixed Points with Applications to Best Simultaneous Approximations}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {1}, pages = {1--12}, 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].}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2012.v28.n1.1}, url = {http://global-sci.org/intro/article_detail/ata/4535.html} }
Copy to clipboard
The citation has been copied to your clipboard