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COMMON FIXED POINT THEOREMS FOR WEAKLY SUBSEQUENTIALLY CONTINUOUS MAPPINGS IN FUZZY METRIC SPACES VIA IMPLICIT RELATION

Yıl 2018, Cilt: 8 Sayı: 1.1, 284 - 294, 01.09.2018

Öz

The aim of this paper is to prove some common xed point theorems for two weakly subsequentially continuous and compatible of type E pairs of self mappings satisfying an implicit relation in fuzzy metric spaces. Two examples are given to illustrate our results.

Kaynakça

  • [1] Abbas, M., Imdad, M., Gopal, D., 8 (5) (2011), ψ-weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 141-148.
  • [2] Altun, I., T¨urkoˇglu,D., (2008), Some fixed point theorems on fuzzy metric spaces with implicit relations, Commun. Korean Math. Soc. 23, No. 1, 111-124.
  • [3] Beloul, S., 15(2015), Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Appl.Maths E-Notes, 173-186.
  • [4] Bouhadjera, H., GodetThobie, C., (2009), Common fixed point theorems for pairs of subcompatible maps, arXiv:0906.3159 V1 [math.FA]
  • [5] Cho, Y. J., Sedghi, S., Shobe, N., 39 (2009), Generalized fixed point theorems for Compatible mappings with some types in fuzzy metric spaces, Chaos, Solitons and Fractals, 2233-2244.
  • [6] George,A., Veeramani, P., 90,(1997), On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 365-368.
  • [7] Gopal, D., Imdad, M., 57(2) (2011), Some new common fixed point theorems in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 303-316.
  • [8] Grabiec, M., 27 (1988), Fixed point on fuzzy metric spaces, Fuzzy Sets Syst., 385-389.
  • [9] Imdad, M., Ali, J., Tanveer, M., 24(2011), Remarks on some recent metrical common fixed point theorems, Appl. Math. Lett., 1165-1169.
  • [10] Jungck, G., 83(4)(1976), Commuting mappings and fixed points, Amer. Math. Monthly, 261-263.
  • [11] Jungck, G., 9 (1986), Compatible mappings and common fixed points, Int. J. Math. Sci., 771-779.
  • [12] Jungck, G., Rhoades, B. E., 29 (3),(1998), Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 227-238.
  • [13] Kramosil, I., Michalek, J., 11 (1975), Fuzzy metric and statistical metric spaces, Kybernetica, 336-344.
  • [14] Mishra, S. N., Sharma, N., Singh, S.L., 17 (1994), Common fixed point of maps on fuzzy metric spaces, Internat. J. Math. Math. Sci., 253-258.
  • [15] Popa, V., (2005), A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat n. 19., 45-51.
  • [16] Rani,A., Kumar, S., (2011), Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation, Int.J. Comput. Appl , Vol 20, no.7., 0975-8887.
  • [17] Saleem, N., Ali, B., Abbas, M., Raza, Z., (2015) 2015:36, Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications, Fixed Point Theory and Applications. [18] Schweizer, B., Sklar, A., (1960), Statistical metric spaces, Pac. J. Math. 10, 314-334.
  • [19] Singh, M. R., Mahendra Singh,Y., (2007), Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type, Inter J. Math. Sci. Engg. Appl. 1 (2), 299-315.
  • [20] Singh, M. R., Mahendra Singh,Y, ,(2011), On various types of compatible maps and common fixed point theorems for non-continuous maps, Hacet. J. Math. Stat.40(4), 503-513.
  • [21] Singh, B., Chouhan, M. S., (2000), Common fixed points of compatible maps in Fuzzy metric spaces, Fuzzy sets and systems, 115, 471-475.
  • [22] Singh, B., Jain, A., Masoodi,A. A., (2010), Semi-compatibility, weak compatibility and fixed point theorem in fuzzy metric space, International Mathematical Forum, 5 (61), 3041-3051.
  • [23] Vasuki, R., (1999), Common fixed points for R-weakly commuting maps in Fuzzy metric spaces, Indian J. Pure Appl. Math. 30(4), 419-423.
  • [24] Zadeh, L. A., (1965) Fuzzy sets, Inform. and control 89, 338-353.
Yıl 2018, Cilt: 8 Sayı: 1.1, 284 - 294, 01.09.2018

Öz

Kaynakça

  • [1] Abbas, M., Imdad, M., Gopal, D., 8 (5) (2011), ψ-weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 141-148.
  • [2] Altun, I., T¨urkoˇglu,D., (2008), Some fixed point theorems on fuzzy metric spaces with implicit relations, Commun. Korean Math. Soc. 23, No. 1, 111-124.
  • [3] Beloul, S., 15(2015), Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Appl.Maths E-Notes, 173-186.
  • [4] Bouhadjera, H., GodetThobie, C., (2009), Common fixed point theorems for pairs of subcompatible maps, arXiv:0906.3159 V1 [math.FA]
  • [5] Cho, Y. J., Sedghi, S., Shobe, N., 39 (2009), Generalized fixed point theorems for Compatible mappings with some types in fuzzy metric spaces, Chaos, Solitons and Fractals, 2233-2244.
  • [6] George,A., Veeramani, P., 90,(1997), On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 365-368.
  • [7] Gopal, D., Imdad, M., 57(2) (2011), Some new common fixed point theorems in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 303-316.
  • [8] Grabiec, M., 27 (1988), Fixed point on fuzzy metric spaces, Fuzzy Sets Syst., 385-389.
  • [9] Imdad, M., Ali, J., Tanveer, M., 24(2011), Remarks on some recent metrical common fixed point theorems, Appl. Math. Lett., 1165-1169.
  • [10] Jungck, G., 83(4)(1976), Commuting mappings and fixed points, Amer. Math. Monthly, 261-263.
  • [11] Jungck, G., 9 (1986), Compatible mappings and common fixed points, Int. J. Math. Sci., 771-779.
  • [12] Jungck, G., Rhoades, B. E., 29 (3),(1998), Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 227-238.
  • [13] Kramosil, I., Michalek, J., 11 (1975), Fuzzy metric and statistical metric spaces, Kybernetica, 336-344.
  • [14] Mishra, S. N., Sharma, N., Singh, S.L., 17 (1994), Common fixed point of maps on fuzzy metric spaces, Internat. J. Math. Math. Sci., 253-258.
  • [15] Popa, V., (2005), A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat n. 19., 45-51.
  • [16] Rani,A., Kumar, S., (2011), Common Fixed Point Theorems in Fuzzy Metric Space using Implicit Relation, Int.J. Comput. Appl , Vol 20, no.7., 0975-8887.
  • [17] Saleem, N., Ali, B., Abbas, M., Raza, Z., (2015) 2015:36, Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications, Fixed Point Theory and Applications. [18] Schweizer, B., Sklar, A., (1960), Statistical metric spaces, Pac. J. Math. 10, 314-334.
  • [19] Singh, M. R., Mahendra Singh,Y., (2007), Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type, Inter J. Math. Sci. Engg. Appl. 1 (2), 299-315.
  • [20] Singh, M. R., Mahendra Singh,Y, ,(2011), On various types of compatible maps and common fixed point theorems for non-continuous maps, Hacet. J. Math. Stat.40(4), 503-513.
  • [21] Singh, B., Chouhan, M. S., (2000), Common fixed points of compatible maps in Fuzzy metric spaces, Fuzzy sets and systems, 115, 471-475.
  • [22] Singh, B., Jain, A., Masoodi,A. A., (2010), Semi-compatibility, weak compatibility and fixed point theorem in fuzzy metric space, International Mathematical Forum, 5 (61), 3041-3051.
  • [23] Vasuki, R., (1999), Common fixed points for R-weakly commuting maps in Fuzzy metric spaces, Indian J. Pure Appl. Math. 30(4), 419-423.
  • [24] Zadeh, L. A., (1965) Fuzzy sets, Inform. and control 89, 338-353.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

- S.beloul Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 1.1

Kaynak Göster