QUADRUPLE FIXED POINT THEOREMS FOR (α,ψ) - CONTRACTIVE TYPE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
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Abstract
In this paper, we determine some quadruple fixed point theorems for nonlinear contractive mappings in the framework of a metric space enclosed with partial order. We prove the uniqueness of a quadruple fixed point for such mappings in this setup. Also, we introduce some examples to illustrate the effectiveness of our results.
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References
. E.S.Wolk, “continuous convergence in partially ordered sets†General Topology and its Applications, Vol. 5, no. 3, pp. 221-234, 1975.
. B. Monjardet, “Metrics on partially ordered sets –a survey,†Discrete mathematics, vol. 35, pp. 173-184, 1981.
. A. C. M. Ran and M. C. B. Reurings, “ A fixed point theorem in partially ordered sets and some applications to matrix equations,†proceedings of the American Mathematical society, vol. 132, no. 5, pp. 1435-1443, 2004.
. T. Gnana Bhaskar and V. Lakhmikantham, “Fixed point theorems in partially ordered metric spaces and applications,†Nonlinear Analysis, Vol. 65, no. 7, pp. 1379-1393, 2006.
. V. Berinde and M. Borcut, “Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,†Nonlinear Analysis, Vol. 74, no. 15, pp. 4889-4897,2011.
. E. Karapinar, “Quartet fixed point for nonlinear contraction,†http//arxiv. Org./ abs/ 1106.5472.
. E. Karapinar and N. V. Luong, “Quadruple fixed point theorems for nonlinear contractions,†computers and mathematics with Applications, Vol. 64, pp. 1839-1848, 2012.
. E. Karapinar, “A new quartet fixed point theorems for nonlinear contractions,†Journal of fixed point Theory and Application, Vol. 6, no. 2, pp. 119-135, 2011.
Mohammad Mursaleen, Syed Abdul Mohiuddine, Ravi P. Agarwal, “Coupled Fixed Point Theorems for(α,ψ) - Contractive Type Mappings in Partially Ordered Metric Spacesâ€, Fixed Point Theory and Applications 2012, 2012:228, doi:1186/1687-1812-2012-228.