Common Fixed Point Theorems for R-weakly Commuting Maps Satisfying Common Property (E.A.) in Intuitionistic Fuzzy Metric Spaces Using Implicit Relation


Affiliations

  • Thapar University, School of Mathematics and Computer Applications, Patiala, India
  • V.S.K.C. Government Degree College, Dehradun, India

Abstract

The aim of this paper is to extend and generalize the theory of fixed point to theory of intuitionistic fuzzy fixed point. We prove common fixed point theorems for R-weakly commuting maps employing common property (E.A) in intuitionistic fuzzy metric space via implicit relations which are viable, productive and powerful tool in finding the existence of common fixed point. Our results unify and generalize various known results to more general class of noncompatible maps.

Keywords

Intuitionistic Fuzzy Metric Space, R-Weakly Commuting Maps, Property (E.A.), Common Property (E.A.), Implicit Relation.

Subject Discipline

Mathematical Sciences

Full Text:

References

M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181–188.

C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces,Chaos, Solitons and Fractals, 29(2006), 1073–1078.

K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87–96.

D. Coker, An introduction to Intuitionistic Fuzzy topological spaces, Fuzzy Sets and System, 88(1997), 81– 89.

J. X. Fang and Y. Gao, Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Analysis, 70 (1)(2009), 184–193.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994),395–399.

M. Imdad, M. Tanveer and M. Hasan, Some common fixed point theorems in Menger,PM-spaces, Fixed Point Theory and Applications, Volume 2010, Article ID 819269, 14 pages.

G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771–779.

G. Jungck and B.E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227–238.

I. Kramosil and J. Michalek, Fuzzy metric and statistical spaces, Kybernetica, 11 (1975), 336–344.

S. Kumar, Common fixed point theorems in intuitionistic fuzzy metric spaces using property (E.A), J. Indian Math. Soc., 76 (1-4) (2009), 94–103.

S. Kumar and B. Fisher, A common fixed point theorem in fuzzy metric space using property (E.A) and implicit relation, Thai J. Math., 8 (3) (2010), 439–446.

W. Lui, J. Wu and Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci, 19, 2005, 3045–3055.

K. Menger, Statistical metrics, Proc. Nat. Acad.Sci.(USA),28 (1942), 535–537.

D. Mihet, Fixed point theorems in fuzzy metric spaces using property E.A., Nonlinear Analysis, 73 (7) (2010), 2184–2188.

R. P. Pant, Common fixed points of contractive maps, J. Math. Anal. Appl., 226 (1998), 251–258.

J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitions and Fractals, 22(2004), 1039–1046.

B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland Amsterdam, 1983.

S. Sessa, On a weak commutativity condition in fixed point consideration, Publ. Inst. Math. (Beograd), 32(46) (1982),146–133.

S. L. Singh and A. Tomar, Weaker forms of commuting maps and existence of fixed points, J. Korea. Soc. of Math, Educ. Ser. B: Pure Appl. Math., 10(3) (2003), 145–161.

S. L. Singh and A. Tomar, Fixed point theorems on FM-spaces, J. Fuzzy Mathematics IFMI, 12(2004),13–16.

L. A. Zadeh, Fuzzy sets, Infor. and Control., 8(1965), 338–353.


Refbacks

  • There are currently no refbacks.