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2011, vol. 15, iss. 2, pp. 65-68
On a statement by I. Aranđelović for asymptotic contractions in Appl. Anal. Discrete Math.
University of Belgrade, Faculty of Mathematics

emailandreja@predrag.us
Keywords: metric and topological spaces; TCS-convergence; complete spaces; contraction; asymptotic contraction; nonlinear conditions for fixed points; kirk'stheorem for asymptotic contractions; Taskovic's characterizations of asymptotic conditions for fixed points
Abstract
We prove that main result of asymptotic contractions by I. Aranđelović [Appl. Anal. Disrete Math. 1 (2007), 211-216, Theorem 1, p. 212] has been for the first time proved 21 years ago in Tasković [Fundamental elements of the fixed point theory, ZUNS- 1986, Theorem 4, p. 170]. But, the author (and next other authors) this historical fact is to neglect and to ignore.
References
Aranđelović, I.D. (2007) Note on asymptotic contractions. Applicable Analysis and Discrete Mathematics, vol. 1, br. 1, str. 211-216
Chen, Y.Z. (2005) Asymptotic fixed points for nonlinear contractions. Fixed point Theory Appl, 2, 213-217
Ivanov, A.A. (1976) Isledovanii po topologii-II. in: Zapiski naučnih seminarov lomi, Lenjingrad, 66, 5-102
Jachymski, J., Jozwik, I. (2004) On Kirk's asymptotic contractions. J Math. Anal. Appl, 300, 147-159
Kirk, W.A. (2003) Fixed points of asymptotic contractions. J Math. Anal. Appl, 277, 645-650
Tasković, M.R. (1986) Fundamental elements of the fixed point theory. Beograd: Zavod za udžbenike i nastavna sredstva, in Serbian
Tasković, M.R. (1985) A characterization of the class of contraction type mappings. Kobe J. Math, 2, 45-55
Tasković, M.R. (1993) Nonlinear functional analysis: Fundamental elements of theory. Beograd: Zavod za udžbenike i nastavna sredstva
Tasković, M.R. (2008) On Kirk's fixed point main theorem for asymptotic contractions. Mathematica Moravica, br. 12-2, str. 45-49
Wong, C.S. (1975) Maps of contractive type. in: Seminar of Fixed Point Theory and its Appl., June, Proc, Dalhousie University, str. 197-207
 

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article language: English
document type: unclassified
DOI: 10.5937/MatMor1102065T
published in SCIndeks: 27/03/2012

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