Some Remarks on Multidimensional Fixed Point Theorems in Partially Ordered Metric Spaces.
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2014, Vol 7, Issue 1
Abstract
In this paper , we show that multidimensional ( coupled, tripled, quadrupled, n-tupled) theorems can be reduced to unidimensional fixed point theorems. . Our results generalize, extend and improve the coupled fixed point results of Bhaskar and Lakshmikantham, Nonlinear Analysis: Theory, Methods and Applications, vol.65, no.7, 2006, pp. 1379-1393, V. Lakshmikantham and L. Ciric, Nonlinear Analysis, Theory, Method and Applications, vol. 70, no12, 2009, pp. 4341-4349, tripled fixed point result by Berinde and Borcut, Nonlinear Analysis, Volume 74, Issue 15, October 2011, Pages 4889-4897, Quadruple fixed point theorems by E. Karapinar and V. Berinde, Banach Journal of Mathematical Analysis, vol. 6, no.1, pp. 74-89, 2012 and multidimensional fixed point results by Muzeyyen Erturk and Vatan Karakaya, Journal of Inequalities and Applications 2013, 2013:196, pp. 1-19, M. Imdad, A. H.Soliman, B. S. Choudhary and P. Das, Journal of Operators, Volume 2013, Article ID 532867, pp. 1-8 and M. Paknazar, M. E. Gordji, M. D. L. Sen and S. M. Vaezpour, Fixed Point Theory and Applications 2013, 2013:11 etc.
Authors and Affiliations
Sumitra Dalal, Ibtisam Masmali, Liaqat Ali Khan, Stojan Radenovic
Keywords
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- EP ID EP651236
- DOI 10.24297/jam.v7i1.2582
- Views 214
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