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2011, vol. 15, iss. 1, pp. 53-57
On a result of T. Suzuki for generalized distance and fixed points
University of Belgrade, Faculty of Mathematics

emailandreja@predrag.us
Keywords: fixed points; τ-distance; complete metric spaces; topological spaces; localization monotone principle; TCS-convergence; nonlinear conditions for fixed points; Tasković's localization monotone principle of fixed point
Abstract
We prove that a main result of T. Suzuki [J. Math. Anal. Appl. 253 (2001), 440-458, Theorem 1, p. 451] has been for the first time proved 20 years ago by Tasković [Proc. Amer. Math. Soc. 94 (1985), 427-432, Theorem 2, p. 430], and second time proved by Tasković [Math. Japonica, 35 (1990), 645-666, Theorem 2, p. 654] as a very special case of the so-called Localization Monotone Principle.
References
Dugundji, J., Granas, A. (1978) Weakly contractive maps and elementary domain invariance theorem. Bull. Soc. Math. Grece (N.S.), 19, 1, 141-151
Suzuki, T. (2001) Generalized Distance and Existence Theorems in Complete Metric Spaces. Journal of Mathematical Analysis and Applications, 253(2): 440-458
Tasković, M.R. (1985) A monotone principle of fixed points. Proc. Amer. Math. Soc., 94, 3, 427-432
Tasković, M.R. (1990) Some new principles in fixed point theory. Mathematica Japonica, 35, 4, 645-666
 

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article language: English
document type: unclassified
DOI: 10.5937/MatMor1101053T
published in SCIndeks: 27/03/2012

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