Discontinuity and R-weak commutativity in fixed point consideration on non complete fuzzy metric spaces
Abstract
Abstract:In this paper we prove common fixed point theorem under the condition of R-weak commutativity without taking any function continuous. We extend results of Sharma and Deshpande [33].
About this article
References
[1] Badard, R: Fixed point theorems for fuzzy number, Fuzzy Sets and Systems, 13(1984), 291-302.
[2] Chang, S.S., Cho, Y.J., Lee, B.S., Jung, J.S. and Kang, S.M.: Coincidence point and minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems 88(1) (1997), 119-128.
[3] Cho, Y. J.: Fixed points in fuzzy metric spaces, J. Fuzzy Math., 5(4) (1997), 949- 962.
[4] Cho, Y.J.,Pathak, H.K., Kang, S.M. and Jung, J.S. : Common fixed points of compatible maps of type () on fuzzy metric spaces, Fuzzy Sets and Systems, 93(1998), 99-111.
[5] Chugh, R. and Kumar, S.: Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci.), 111(2) (2001), 241-247.
View more references (37)
[6] Deng, Z. K. : Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86(1982), 74-95
[7] Erceg, M. A.:Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69(1979), 205-230.
[8] Fang, J. X.: On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46(1992), 107-113.
[9] George, A. and Veeramani, P.: On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(1994), 395-399.
[10] Grabiec, M.: Fixed point in fuzzy metric space, Fuzzy Sets and Systems, 27(1988), 385-389.
[11] Hadzic, O.: Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces, Fuzzy Sets and Systems, 29(1989), 115-125.
[12] Hadzic, O.: Fixed Point Theorems in Probabilistic Metric Spaces, Serbian Academy of Sciences and Arts, Institute of Mathematics, University of Novisad, Yugoslovia. 1995.
[13] Iseki, K.: Some applications of banach type contraction principles, Math. Sem. Notes. Kobe Univ., 4 (1976), 211-214.
[14] Istratescu, I.: A fixed point theorem for mappings with a probabilistic contractive iterates, Rev. Roumaire. Math. Pure Appl., 26(1981), 431-435.
[15] Jung, J. S., Cho, Y. J. and Kim, J. K.: Minimization theorems for fixed point theorems in fuzzy metric spaces and applications, Fuzzy Sets and Systems, 61(1994), 199-207.
[16] Jung, J. S., Cho, Y. J., Chang, S. S. and Kang, S. M.: Coincidence theorems for set-valued mappings and Ekelands variational principle in fuzzy metric spaces, Fuzzy sets and Systems, 79(1996), 239-250.
[17] Jungck, G.: Commuting mappings and fixed points, Amer. Math. Monthly, 83(1976), 261-263.
[18] Jungck, G.: Commuting mappings and fixed points, Amer. Math. Monthly, 83(1976), 261-263.
[19] Jungck, G.: Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103(1988), 977-983.
[20] Jungck, G., Murthy, P. P. and Cho, Y.J.: Compatible mappings of type (A) and common fixed points, Math.Japon., 38(2) (1993), 381-390.
[21] Jungck G., and Rhoades, B. E.: Fixed point for set valued functions without continuity, Ind. J. Pure Appl. Maths., 29(3)(1998), 227-238.
[22] Kaleva, O. and Seikkala, S.: On fuzzy metric spaces, Fuzzy Sets and Systems, 12(1984), 215-229.
[23] Kannan,R.: Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.
[24] Kramosil, I. and Michalek, J.: Fuzzy metric and statistical metric spaces, Kybernetika, 11(1975), 336-344.
[25] Mishra, S. N., Sharma, N. and Singh, S. L.: Common fixed points of maps in fuzzy metric spaces. Internat. J. Math. Math. Sci., 17(1994), 253-258.
[26] Pant, R.P.: Common fixed points of non commuting mappings, J. Math. Anal. Appl., 188(1994), 436-440.
[27] Pathak, H.K.,Cho,Y.J., Chang,S.S. and Kang, S.M.: Compatible Mappings of Type (P), Rev. Res. Univ. Novisad to Apper.
[28] Rhoades,B.E.: A Comparison of Various definitions of contractive mappings, Trans, Amer. Math. Soc., 226(1977), 257-290.
[29] Rhoades, B.E.:Contractive definitions revisited, Contemp. math., 21 (1983), 313-334.
[30] Schweizer, B. and Sklar, A.: Statistical metric spaces, Pacific. J. Math., 10(1960), 313-334.
[31] Sessa, S.: On weak commutativity condition of mappings in a fixed points considerations, Publ. Inst. Mat., 32(46) (1982), 149-153.
[32] Sessa, S., Rhoades, B.E. and Khan, M.S.: On common fixed points of compatible mappings in metric space and Banach space, Internat. J. Math.Math. Sci., 11(1988), 375-392.
[33] Sharma, Sushil and Deshpande, B.: Discontinuity and weak compatibility in fixed point consideration on non – complete fuzzy metric spaces, J. Fuzzy Math., Vol. 11 No. 2 (2003), 671-686.
[34] Singh, S.L.: Some common fixed pint theorems in L-spaces, Math. Sem. Notes. Kobe Univ., 7 (1979), 91-97.
[35] Singh, S.L. and Kasahara,S.: On some recent results on common fixed points, Indian J.Pure Appl., Maths., 13 (1982), 757-761, Corrigendum, 14 (1983), 1075.
[36] Singh, S.L. and Ram, B.: common fixed pints commuting mappings in 2 metric spaces, Math. Sem. Notes Kobe Univ., 10 (1982), 197-208.
[37] Sharma, Sushil : On fuzzy metric space, Southeast Asian Bull. Math.,Springer-Verlag, Vol. 6, No. 1 (2002), 145-157.
[38] Sharma, Sushil: Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems. 125 (2001), 1-8.
[39] Sharma, Sushil and Deshpande, B.: Common fixed point of compatible maps of type (β) on fuzzy metric space, Demonstratio Math., Vol. 35, No. 1 (2002), 165-174.
[40] Tivari, B.M.L. and Singh, S.L.: A. note on recent genralization of jungck contraction principle J. UPGC. Soc., 3 (1986), 13-19.
[41] Vasuki, R.: Common fixed point for R-weakly commuting maps in fuzzy metric spaces, Ind. J. Pure Appl. Math. 30(1999), 419-423.
[42] Zadeh, L.A.: Fuzzy Sets, Inform Contr., 8(1965), 338-353.