Common fixed point and invariant approximation results on non-starshaped domains

Georgian Mathematical Journal

Volumn 12, Issue 4, 2005, Pages 659-669

  Hussain, Nawab ^a   O'REGAN, Donal ^b   Agarwal, Ravi P ^c  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c Florida Institute of Technology ^*  (United States)

Author keywords

approximation results; common; Fixed point theory; invariant; non starshaped domains

Indexed keywords

EID: 33749535484     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.2005.659     Document Type: Article

References (25)

1. M. A. AL-THAGAFI, Common fixed points and best approximation. J. Approx. Theory 85(1996), No. 3, 318-323.
2. D. E. ANDERSON, J. L. Nelson, and K. L. Singh, Fixed points for single and multivalued mappings in locally convex spaces. Math. Japon. 31(1986), No. 5, 665-672.
3. E. BASKARAN AND L. V. SUBRAHMANYAM, Common fixed points in closed balls. Atti Sem. Mat. Fis. Univ. Modena 36(1988), No. 1, 1-5.
4. I. BEG, A. R. Khan, and N. Hussain, Approximation of *-nonexpansive random multivalued operators on Banach spaces. J. Aust. Math. Soc. 76(2004), No. 1, 51-66.
5. B. BROSOWSKI, Fixpunktsätze in der Approximationstheorie. Mathematica (Cluj) 11 (34)(1969), 195-220.
6. W. J. DOTSON, Jr., Fixed point theorems for non-expansive mappings on star-shaped subsets of Banach spaces. J. London Math. Soc. (2) 4(1971/72), 408-410.
7. W. J. DOTSON, Jr., On fixed points of nonexpansive mappings in nonconvex sets. Proc. Amer. Math. Soc. 38(1973), 155-156.
8. L. HABINIAK, Fixed point theorems and invariant approximations. J. Approx. Theory 56(1989), No. 3, 241-244.
9. T. L. HICKS AND M. D. HUMPHRIES, A note on fixed-point theorems. J. Approx. Theory 34(1982), No. 3, 221-225.
10. N. HUSSAIN AND A. R. KHAN, Common fixed-point results in best approximation theory. Appl. Math. Lett. 16(2003), No. 4, 575-580.
11. G. JUNGCK AND S. SESSA, Fixed point theorems in best approximation theory. Math. Japon. 42(1995), No. 2, 249-252.
12. A. R. KHAN, N. Hussain, and L. A. Khan, A note on Kakutani type fixed point theorems. Int. J. Math. Math. Sci. 24(2000), No. 4, 231-235.
13. G. MEINARDUS, Invarianz bei linearen Approximationen. Arch. Rational Mech. Anal. 14(1963), 301-303.
14. S. A. NAIMPALLY, K. L. Singh, and J. H. M. Whitfield, Fixed points and nonexpansive retracts in locally convex spaces. Fund. Math. 120(1984), No. 1, 63-75.
15. R. P. PANT, Common fixed points of noncommuting mappings. J. Math. Anal. Appl. 188(1994), No. 2, 436-440.
16. W. RUDIN, Functional analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973.
17. S. A. SAHAB, M. S. Khan, and S. Sessa, A result in best approximation theory. J. Approx. Theory 55(1988), No. 3, 349-351.
18. B. N. SAHNEY, K. L. Singh, and J. H. M. Whitfield, Best approximations in locally convex spaces. J. Approx. Theory 38(1983), No. 2, 182-187.
19. N. SHAHZAD, A result on best approximation. Tamkang J. Math. 29(1998), No. 3, 223-226; correction in Tamkang J. Math. 30(1999), No. 2, 165.
20. N. SHAHZAD, Noncommuting maps and best approximations. Rad. Mat. 10(2000/01), No. 1, 77-83.
21. N. SHAHZAD, Invariant approximations and R-subweakly commuting maps. J. Math. Anal. Appl. 257(2001), No. 1, 39-45.
22. N. SHAHZAD, Generalized I-nonexpansive maps and best approximations in Banach spaces. Demonstratio Math. 37(2004), No. 3, 597-600.
23. S. P. SINGH, An application of a fixed-point theorem to approximation theory. J. Approx. Theory 25(1979), No. 1, 89-90.
24. P. V. SUBRAHMANYAM, An application of a fixed point theorem to best approximation. J. Approximation Theory 20(1977), No. 2, 165-172.
25. K. K. TAN AND X. Z. YAUN, Random fixed-point theorems and approximation in cones. J. Math. Anal. Appl. 185(1994), No. 2, 378-390.