JOURNAL OF ADVANCES IN MATHEMATICS · 2014 · 19 citations · 20 references
Social SciencesComputer ScienceAxonometric ProjectionComputational GeometryMultivariate VisualizationExistence TheoremsFixed Point TheoryFixed PointsMetric GeometryBanach Fixed Point TheoremCoupled Fixed PointsExistence Of Fixed PointsNonlinear AnalysisOrdered Metric Spaces
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 theorems 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.
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