COMMENTS ON THE PAPERS ARCH. MATH. BRNO, 422006, 51-58 - THAI J. MATH., 32005, 63-70 AND MATH. COMMUNICATIONS 132008, 85-96

Volume 2, Issue 3, pp 168-173 http://dx.doi.org/10.22436/jnsa.002.03.04

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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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Keywords

• Dotsons' convexity structure
• Property (A)
• Common fixed point
• Compatible maps.

MSC

•  47H10
•  54H25

References

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• [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.


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• [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)


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