A New Approach to Common Coupled Fixed Point of Caristi Type Contraction on a Metric Space Endowed with a Graph

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper we introduced a new notation G – fg –   contraction of Caristi type and a new edge preserving property. With help of these we proved a some coupled fixed point results for four maps endowed with a graph in a complete metric space. Also we gave an application to integral equations.

     


  • Keywords


    Metric spaces with a graph, edge preserving property, coupled fixed point.

  • References


      [1] Abbas M, Alikhan M, S.Radenovi´ c, “Common coupled fixed point theorems in cone metric spaces for w-compatible mappings”, Applied Mathematics and Computation., Volume 217(2010), Issue 1, 195 - 202.

      [2] Bhaskar TG, Lakshmikantham V, “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Analysis, 65(2006), 1379 - 1393.

      [3] Chifu.C, Petrusel. G, “New results on coupled fixed point theory in metric spaces endowed with a directed graph”, Fixed Point Theory Appl., 151(2014).

      [4] Espinola. R, Kirk. WA, “Fixed point theorems in R-trees with applications to graph theory”, Topol. Appl., 153(2006), 1046-1055.

      [5] Jachymski.J, “The contraction principle for mappings on a metricspace with a graph”, Proc. Am. Math. Soc., 136(4)(2008), 1359-1373.

      [6] j. S. Jung, Y. J. Cho, S. M. Kang, B. S. Lee, and Y. K. Choi, “Coincidence point theorems in generating spaces of quasi metric family”, Fuzzy Sets and Systems., 116(3) (2000),471-479.

      [7] Lakshmikantham V, ´Ciri´c Lj, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Analysis., 70(2009), 4341 - 4349.

      [8] Rao KPR, Kishore GNV, Nguyen Van Luong, “A unique common coupled fixed point theorem for four maps under ψ - φ contractive condition in partial metric spaces”, CUBO A Mathematical Journal., 14(3)(2012), 115 - 127.

      [9] Rao KPR, Kishore GNV, Raju VCC, “A coupled fixed point theorem for two pairs of w - compatible maps using altering distance function in partial metric space”, Journal of Advanced Research in Pure Mathematics., 4(4)(2012), 96 - 114.

      [10] Banach S, “Sur les operations dans les ensembles abstraits et leur application aux equations integrals”, Fund. Math., 3(1)(1922), 133 181.

      [11] Caristi J, “Fixed point theorems for mappings satisfying inwardness conditions”, Transactions of the American Mathematical Society, 215(1976), 241-251.

      [12] Ekeland I, “On the variational principle”, Journal of Mathematical Analysis and Applications., 47(2)(1974), 324-353.

      [13] Bhaskar TG and Lakshmikantham V, “Fixed point theorems in partially ordered cone metric spaces and applications”, Nonlinear Analysis Theory Methods and Applications., 65(7) (2006), 825-832.


 

View

Download

Article ID: 20927
 
DOI: 10.14419/ijet.v7i4.10.20927




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.