COMMENTS ON THE PAPERS ARCH. MATH. BRNO, 422006, 51-58 - THAI J. MATH., 32005, 63-70 AND MATH. COMMUNICATIONS 132008, 85-96
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Authors
N. HUSSAIN
- Department of Mathematics, King Abdul Aziz University P. O. Box 80203, Jeddah 21589 Saudi Arabia..
Abstract
Using Dotsons' convexity structure, the authors in [16, 17, 18]
established some deterministic and random common fixed point results. In this
note, we comment that the proofs of the results in [16, 17, 18] are incomplete
and incorrect.
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ISRP Style
N. HUSSAIN, COMMENTS ON THE PAPERS ARCH. MATH. BRNO, 422006, 51-58 - THAI J. MATH., 32005, 63-70 AND MATH. COMMUNICATIONS 132008, 85-96, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 3, 168-173
AMA Style
HUSSAIN N., COMMENTS ON THE PAPERS ARCH. MATH. BRNO, 422006, 51-58 - THAI J. MATH., 32005, 63-70 AND MATH. COMMUNICATIONS 132008, 85-96. J. Nonlinear Sci. Appl. (2009); 2(3):168-173
Chicago/Turabian Style
HUSSAIN, N.. "COMMENTS ON THE PAPERS ARCH. MATH. BRNO, 422006, 51-58 - THAI J. MATH., 32005, 63-70 AND MATH. COMMUNICATIONS 132008, 85-96." Journal of Nonlinear Sciences and Applications, 2, no. 3 (2009): 168-173
Keywords
- Dotsons' convexity structure
- Property (A)
- Common fixed point
- Compatible maps.
MSC
References
-
[1]
F. Akbar, A. R. Khan, Common fixed point and approximation results for noncommuting maps on locally convex spaces, Fixed Point Theory and Appl., 2009 (2009), in press
-
[2]
I. Beg, A. R. Khan, N. Hussain, Approximation of *-nonexpansive random multivalued operators on Banach spaces, J. Aust. Math. Soc., 76 (2004), 51-66.
-
[3]
V. Berinde, Fixed point theorems for nonexpansive operators on nonconvex sets, Bul.- Stiint.-Univ.-Baia-Mare-Ser.-B, 15 (1999), 27-31.
-
[4]
W. J. Dotson Jr., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc., 38 (1973), 155-156.
-
[5]
N. Hussain , Common fixed point and invariant approximation results, Demonstratio Math., 39 (2006), 389-400.
-
[6]
N. Hussain, Generalized I-nonexpansive maps and invariant approximation results in p- normed spaces, Analysis in Theory and Appl., 22 (2006), 72-80.
-
[7]
N. Hussain, V. Berinde, Common fixed point and invariant approximation results in certain metrizable topological vector spaces, Fixed Point Theory and Appl., 2006 (2006), 13 pages.
-
[8]
N. Hussain, G. Jungck , Common fixed point and invariant approximation results for noncommuting generalized (f; g)-nonexpansive maps, J. Math. Anal. Appl., 321 (2006), 851-861.
-
[9]
N. Hussain, A. R. Khan , Common fixed points and best approximation in p-normed spaces, Demonstratio Math., 36 (2003), 675-681.
-
[10]
N. Hussain, D. O'Regan, R. P. Agarwal, Common fixed point and invariant approximation results on non-starshaped domains, Georgian Math. J., 12 (2005), 659-669.
-
[11]
N. Hussain, B. E. Rhoades, \(C_q\)-commuting maps and invariant approximations, Fixed Point Theory and Appl., 2006 (2006), 9 pages.
-
[12]
A. R. Khan, N. Hussain, A. B. Thaheem, Applications of fixed point theorems to invariant approximation, Approx. Theory and Appl., 16 (2000), 48-55.
-
[13]
A. R. Khan, A. B. Thaheem, N. Hussain, Random fixed points and random approximations in nonconvex domains, J. Appl. Math. Stoch. Anal., 15 (2002), 263-270.
-
[14]
A. R. Khan, A. Latif, A. Bano, N. Hussain, Some results on common fixed points and best approximation, Tamkang J. Math., 36 (2005), 33-38.
-
[15]
R. N. Mukherjee, T. Som , A note on an applications of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math., 16 (1985), 243-244.
-
[16]
H. K. Nashine, Best approximation for nonconvex set in q-normed space, Arch. Math. (BRNO), 42 (2006), 51-58.
-
[17]
H. K. Nashine , Common random fixed point and random best approximation, Thai J. Math., 3 (2005), 63-70.
-
[18]
H. K. Nashine, R. Shrivastava , Common fixed points and best approximants in non- convex domain, Mathematical Communications , 13 (2008), 85-96.
-
[19]
W. Rudin , Functional Analysis, McGraw-Hill, New York (1991)
-
[20]
L. A. Talman, A fixed point criterion for compact \(T_2\)-spaces, Proc. Amer. Math. Soc., 51 (1975), 91-93.