Abstract
Ilić and Rakočević [6] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without using the normality condition but only for a contractive constant λ ∈ (0, 1/2) [8]. In this note, using a new method of proof, we prove this theorem for any contractive constant λ ∈ (0, 1).
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References
M. Abbas and B. E. Rhoades, Appl. Math. Lett., 22:4 (2009), 511–515.
C. D. Bari and P. Vetro, Rend. Circ. Mat. Palermo, 57:2 (2008), 279–285.
Lj. B. Ćirić, Proc. Amer. Math. Sc., 45 (1974), 267–273.
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
L.-G. Huang and X. Zhang, J. Math. Anal. Appl., 332:2 (2007), 1468–1476.
D. Ilić and V. Rakočević, Appl. Math. Lett., 22:5 (2009), 728–731.
G. Jungck, S. Radenović, S. Radojević, and V. Rakočević, Fixed Point Theory and Applications, 2009, Art. ID 643640, doi: 10.1155/2009/643640.
Z. Kadelburg, S. Radenović, and V. Rakočević, Appl. Math. Lett., 22:11 (2009), 1674–1679.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 1, pp. 75–79, 2012
Original Russian Text Copyright © by Ljiljana Gajić and Vladimir Rakočević
Supported by Grant No. 174025 of the Ministry of Science, Technology, and Development, Republic of Serbia.
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Gajić, L., Rakočević, V. Quasi-contractions on a nonnormal cone metric space. Funct Anal Its Appl 46, 62–65 (2012). https://doi.org/10.1007/s10688-012-0008-2
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DOI: https://doi.org/10.1007/s10688-012-0008-2