International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.3, Jun. 2015, Pub. Date: May 16, 2015
Fixed Point Theorems in Fuzzy Normed Spaces for Weak Contractive Mappings
Pages: 111-115 Views: 1296 Downloads: 531
[01] S. A. M. Mohsenialhosseini, Faculty of Mathematics, Vali-e-Asr University, Rafsanjan‎, ‎Iran.
We define fixed point ‎for ‎the class of weak contractive type ‎mappings‎ in fuzzy normed spaces‎. We obtain several convergence theorems for fixed points by means of Picard ‎iteration on fuzzy normed ‎spaces. ‎These ‎extend the corresponding results in literature by providing error estimates, rate of convergence for the used iterative method as well as results concerning the data dependence of the fixed ‎points on fuzzy norm ‎spaces‎.
‎‎‎Fuzzy Normed Space, Fuzzy Fixed Point, Weak Contraction, Convergence Theorem
[01] H. Amann, Fixed point equations and nonlinear eigenvalue problems inor4'ed Banach spaces, SIAM Rev., 18(2) (1976), 620-709.
[02] J. Franklin, Methods of Mathematical Economics, Springer Verlag, New York, (1980).
[03] S.A.M. Mohsenalhosseini, H. Mazaheri, M.A. Dehghan and M. Bagheshahi, ”Application of Approximate Best Proximity Pairs,” Gen. Math. Notes, Vol. 7, No. 1, pp.59-65, 2011.
[04] S. V. Krishna and K. K.M. Sarma, “Separation of fuzzy normed linear spaces,” Fuzzy Sets and Systems, vol. 63, no. 2, pp. 207-217, 1994.
[05] J.-z. Xiao and X.-h. Zhu, “Fuzzy normed space of operators and its completeness,” Fuzzy Sets and Systems, vol. 133, no. 3, pp. 389–399, 2003.
[06] A. Chitra, P.V., ”Mordeson, ”Fuzzy linear operators and fuzzy normed linear spaces,”Bull. Cal. Math.Soc, vol. 74, pp. 660-665, 1969.
[07] T. Bag, S. K. Samanta, ”Finite dimensional fuzzy normed linear spaces,”J. Fuzzy Math, vol. 11, no. 3, pp. 687-705, 2003.
[08] T. Bag, S. K. Samanta, ”Fuzzy bounded linear opera- tors,”Fuzzy Sets syst, vol. 151, no. 3, pp. 513-547, 2005.
[09] T. Bag, S. K. Samanta, ”Some fixed point theorems in fuzzy normed linear spaces,” Information Sciences, 177 pp. 3271-3289, 2007.
[10] V. Berinde, ”On the Approximation of Fixed Points of Weak Contractive Mappings,” Carpathian J. Math, vol 19, no. 1, pp. 7-22, 2003.
[11] S. A. M. Mohsenalhosseini1 and H.Mazaheri, ” Approx- imate Fixed Point Theorems in Fuzzy normed Spaces s for an Operator,” Advances in Fuzzy Systems, Volume 2013, Article ID 613604, 8 pages.
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