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Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove some new results on the existence of common fixed points for nonexpansive and asymptotically nonexpansive mappings in the framework of convex metric spaces. We also obtain some results on common fixed points from the set of best and best simultaneous approximations as applications. The proved results generalize and extend some of the known results in the literature.
Wydawca
Rocznik
Strony
33--46
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
  • Department of Applied Sciences, Khalsa College of Engineering & Technology, Punjab Technical University, Ranjit Avenue, Amritsar-143001, India, chansok.s@gmail.com
Bibliografia
  • [1] M. A. Al-Thagafi and N. Shahzad, Banach operator pairs, common fixed points, invariant approximations, and *-nonexpansive multimaps. Nonlinear Analysis 69 (2008), 2733-2739.
  • [2] I. Beg and M. Abbas, Common fixed points and best approximation in convex metric spaces, Soochow J. Math. 33 (2007), 729-738.
  • [3] S. Chandok and T. D. Narang, On fixed points and common fixed points of nonex-pansive mappings, Math. Notae 45 (2008), 51-57.
  • [4] S. Chandok and T. D. Narang, Some common fixed point theorems for Banach operator pairs with applications in best approximation. Nonlinear Anal. 73 (2010), 105-109.
  • [5] J. Chen and Z. Li, Common fixed points for Banach operator pairs in best approximations, J. Math. Anal. Appl. 336 (2007), 1466-1475.
  • [6] B. Fisher, Mappings with a common fixed point. Math. Sent. Notes Kobe Univ. 1 (1979), 81-84.
  • [7] M. D. Guay, K. L. Singh and J. H. M. Whitfield, Fixed point theorems for nonex-pansive mappings in convex metric spaces, in: Nonlinear Analysis and Applications, Lect. Notes Pure Appl. Math. 80, Marcel Dekker (1982), 179-189.
  • [8] S. Itoh, Some fixed point theorems in metric spaces, Fund. Math. 52 (1979), 109-117.
  • [9] G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. American Math. Soc. 103 (1988), 977-983.
  • [10] G. Jungck and B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), 227-238.
  • [11] A. R. Khan and F. Akbar, Common fixed points from best simultaneous approximation, Taiwanese J. Math. 13 (2009), 1379-1386.
  • [12] T. D. Narang and S. Chandok, Common fixed points and invariant approximation of R-subweakly commuting maps in convex metric spaces, Ukrainian Math. J. 62 (2010), 1367-1376.
  • [13] T. D. Narang and S. Chandok, Some fixed point theorems with applications to best simultaneous approximations, J. Nonlinear Sci. Appl. 3 (2010), 87-95.
  • [14] R. R Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994), 436-M0.
  • [15] S. A. Sahab, M. S. Khan and S. Sessa, A result in best approximation theory, J. Approx. Theory 55 (1988), 349-351.
  • [16] N. Shahzad, Invariant approximations and R-subweakly commuting maps, J. Math. Anal. Appl. 257 (2001), 39-45.
  • [17] W. Takahashi, A convexity in metric space and nonexpansive mappings I, Kodai Math. Sent. Rep. 22 (1970), 142-149.
  • [18] P. Vijayaraju, Applications of fixed point theorems to best simultaneous approximations, Indian J. Pure Appl. Math. 24 (1993), 21-26.
  • [19] P. Vijayaraju and M. Marudai, Some results on common fixed points and best approximations, Indian J. Math. 46 (2004), 233-244.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0028
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