Fixed Point Theory, 15(2014), No. 1, 67-78 http://www.math.ubbcluj.ro/ ∼ nodeacj/sfptcj.html COINCIDENCE POINT THEOREMS FOR MULTI-VALUED MAPPINGS IN FUZZY METRIC SPACES TATJANA DO ˇ SENOVI ´ C * AND IVANA ˇ STAJNER-PAPUGA ** * Faculty of Technology University of Novi Sad, Serbia E-mail: tatjanad@tf.uns.ac.rs ** Department of Mathematics and Informatics University of Novi Sad, Serbia E-mail: stajner.papuga@dmi.uns.ac.rs Abstract. In this paper, by applying the countable extensions of a t-norm, we have proved a coincidence point theorem for the fuzzy Nadler type of contraction mappings. Also, a coincidence point theorem in a fuzzy metric spaces for an implicit relation is given. Key Words and Phrases: fuzzy metric space, t-norm, Nadler contraction mapping, coincidence point, Cauchy sequence, implicit relation. 2010 Mathematics Subject Classification: 47H10, 54H25; 55M20. Acknowledgment. The authors are supported by MNTRRS-174009 and by the Provincial Secretariat for Science and Technological Development of Vojvodina. References [1] Lj. ´ Ciri´ c, Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces, Chaos, Solitons and Fractals, 42(2009), 146-154. [2] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(1994) 395-399. [3] A. George , P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90(1997) 365-368. [4] O. Hadˇ zi´ c, A fixed point theorem in Menger spaces, Publ. Inst. Math. Beograd T, 20(1979), 107-112. [5] O. Hadˇ zi´ c, On coincidence point theorem for multivalued mappings in probabilistic metric spaces, Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak., Ser. Mat., 25(1995), 1-7. [6] O. Hadˇ zi´ c, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Pub- lishers, Dordrecht, 2001. [7] O. Hadˇ zi´ c, E. Pap, M. Budinˇ cevi´ c, Countable extension of triangular norms and their applica- tions to the fixed point theory in probabilistic metric spaces, Kybernetika, 38(2002), 363-382. [8] O. Hadˇ zi´ c, E. Pap, Probabilistic multi-valued contractions and decomposable measures, Inter- national J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 10(2002), no. supp. 01, 59-74. [9] O. Hadˇ zi´ c, E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets and Systems, 127(2002), 333344. [10] Y. Liu, Z. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, Fuzzy Sets and Systems, 158(2007), 58-70. 67