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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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