Research Article
BibTex RIS Cite

Sabit Fuzzy Nokta Teoremleri

Year 2020, Volume: 10 Issue: 3, 641 - 650, 15.07.2020
https://doi.org/10.17714/gumusfenbil.621967

Abstract

Bu çalışmada, fuzzy alt kümeler ailesi üzerinde verilmiş olan Hausdorrf fuzzy metrik
uzaylarda, uzaklığı değiştiren fonksiyonlar yardımıyla ilk olarak fuzzy
fonksiyonları için sabit fuzzy nokta teoremi ispatlanmış ve teorem örneklerle
desteklenmiştir. Daha sonra, ana teoremin bir uygulaması olarak ortak sabit
fuzzy nokta teoremi ve ispatı verilmiştir.



 

References

  • Abbas, M., Ali, B. and Vetro, C., 2015. Fixed Fuzzy Points of Fuzzy Mappings in Hausdorff Fuzzy Metric Spaces with Application. Iranian Journal of Fuzzy Systems, 12(3), 31-45.
  • Alaca, C., 2009. On Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Communications of the Korean Mathematical Society, 24(4), 565-579.
  • Ali, B. and Abbas, M., 2013. Suzuki Type Fixed Point Theorem for Fuzzy Mappings in Ordered Metric Spaces. Fixed Point Theory and Applications, 2013:19, 1-19.
  • Chang, C. L., 1968. Fuzzy Topological Space. Journal of Mathematical Analysis and Applications, 24, 182-190.
  • Chitra, A. and Subrahmanyam P. V., 1987. Fuzzy Sets and Fixed Points. Journal of Mathematical Analysis and Applications, 124, 584-590.
  • Dosenovic, T., Rakic, D., Brdar, M., 2014. Fixed Point Theorems in Fuzzy Metric Spaces Using Altering Distance. Filomat, 28(7), 1517-1524.
  • Estruch, V. D. and Vidal, A., 2001. A Note on Fixed Fuzzy Points for Fuzzy Mappings. Rendiconti dell’Istituto di Matematica dell’Universita di Trieste, 32, 39-45.
  • George, A. and Veeramani, P.,1994. On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 64, 395-399.
  • Grabiec, M., 1988. Fixed Points in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 27, 385-389.
  • Gregori, V., Morillas, S. and Sapena, A., 2011. Examples of Fuzzy Metrics and Applications. Fuzzy Sets and Systems, 170, 95-111.
  • Haghi, R. H., Rezapour, Sh.and Shahzad, N., 2011. Some Fixed Point Generalizations are not Real Generalizations. Nonlinear Analysis, 74(5), 1799-1803.
  • Heilpern, S., 1981. Fuzzy Mappings and Fixed Point Theorem. Journal of Mathematical Analysis and Applications, 83(2), 566-569.
  • Khan, M.S., Swaleh, M. and Sessa, S., 1984. Fixed Point Theorems by Altering Distances Between the Points. Bulletin of the Australian Mathematical Society, 30(1), 1-9.
  • Kramosil, O. and Michalek, J., 1975. Fuzzy Metric and Statistical Metric Spaces. Kybernetica, 11, 326-334.
  • Lowen, R., 1976. Fuzzy Topological Spaces and Fuzzy Compactness. Journal of Mathematical Analysis and Applications, 56, 621-633.
  • Mihet, D., 2004. A Banach Contraction Theorem in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 144, 431-439.
  • Nadler, S. B., 1969. Multivalued Contraction Mappings. Pacific Journal of Mathematics, 30(2), 475-488.
  • Naidu, S. V. R., 2003. Some Fixed Point Theorems in Metric Spaces by Altering Distances. Czechoslovak Mathematical Journal, 53(128), 205-212.
  • Nashine H. K. and Aydi, H., 2013. Coupled Fixed Point Theorems for Conctractions Involving Altering Distances in Ordered Metric Spaces. Mathematical Sciences, 7(20), 2013.
  • Pao-Ming, P. and Ying-Ming, L., 1980. Fuzzy Topology: II. Product and Quotient Spaces. Journal of Mathematical Analysis and Applications, 77, 20-37.
  • Phiangsungnoen, S., Sintunavarat, W. and Kumam, P., 2014. Fuzzy Fixed Point Theorems in Hausdorff Fuzzy Metric Spaces. Journal of Inequalities and Applications, 2014(201), 1-10.
  • Popa, V. and Mocanu, M., 2009. Altering Distance and Common Fixed Points Under Implicit Relations. Hacettepe Journal of Mathematics and Statistics, 38(3), 329-337.
  • Rhoades, B. E., 2001. Some Theorems on Weakly Contractive Maps. Nonlinear Analysis: Theory, Methods and Applications, 47(4), 2683-2693.
  • Rodriguez-Lopez, J. and Romaguera, S., 2004. The Hausdorff Fuzzy Metric on Compact Sets. Fuzzy Sets and Systems, 147, 273-283.
  • Schweizer, B. and Sklar, A., 1960. Statistical Metric Spaces. Pacific Journal of Mathematics, 10, 314-334.
  • Shen, Y., Qiu, D., Chen, W., 2012. Fixed Point Theorems in Fuzzy Metric Spaces. Applied Mathematics Letters, 25, 138-141.
  • Türkoğlu, D., Alaca, C., Cho, Y. J., Yıldız, C., 2006. Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Journal of Applied Mathematics and Computing, 22, 411-424.
  • Veeramani, P., 2001. Best Approximation in Fuzzy Metric Spaces. Journal of Fuzzy Mathematics, 9, 75-80.
  • Wong, C. K., 1974. Fuzzy Topology: Product and Quotient Theorems. Journal of Mathematical Analysis and Applications, 45, 512-521.
  • Zadeh, L. A., 1965. Fuzzy Sets. Information and Control, 8, 338-353.

Fixed Fuzzy Point Theorems

Year 2020, Volume: 10 Issue: 3, 641 - 650, 15.07.2020
https://doi.org/10.17714/gumusfenbil.621967

Abstract

In this
study, firstly, fuzzy fixed point theorem was proved for fuzzy mappings by
altering distance functions in Hausdorff fuzzy metric spaces which are given on
family of fuzzy subsets and the theorem was supported by examples. After that,
common fuzzy fixed point theorem  and its
proof were given as an application of main theorem.

References

  • Abbas, M., Ali, B. and Vetro, C., 2015. Fixed Fuzzy Points of Fuzzy Mappings in Hausdorff Fuzzy Metric Spaces with Application. Iranian Journal of Fuzzy Systems, 12(3), 31-45.
  • Alaca, C., 2009. On Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Communications of the Korean Mathematical Society, 24(4), 565-579.
  • Ali, B. and Abbas, M., 2013. Suzuki Type Fixed Point Theorem for Fuzzy Mappings in Ordered Metric Spaces. Fixed Point Theory and Applications, 2013:19, 1-19.
  • Chang, C. L., 1968. Fuzzy Topological Space. Journal of Mathematical Analysis and Applications, 24, 182-190.
  • Chitra, A. and Subrahmanyam P. V., 1987. Fuzzy Sets and Fixed Points. Journal of Mathematical Analysis and Applications, 124, 584-590.
  • Dosenovic, T., Rakic, D., Brdar, M., 2014. Fixed Point Theorems in Fuzzy Metric Spaces Using Altering Distance. Filomat, 28(7), 1517-1524.
  • Estruch, V. D. and Vidal, A., 2001. A Note on Fixed Fuzzy Points for Fuzzy Mappings. Rendiconti dell’Istituto di Matematica dell’Universita di Trieste, 32, 39-45.
  • George, A. and Veeramani, P.,1994. On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 64, 395-399.
  • Grabiec, M., 1988. Fixed Points in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 27, 385-389.
  • Gregori, V., Morillas, S. and Sapena, A., 2011. Examples of Fuzzy Metrics and Applications. Fuzzy Sets and Systems, 170, 95-111.
  • Haghi, R. H., Rezapour, Sh.and Shahzad, N., 2011. Some Fixed Point Generalizations are not Real Generalizations. Nonlinear Analysis, 74(5), 1799-1803.
  • Heilpern, S., 1981. Fuzzy Mappings and Fixed Point Theorem. Journal of Mathematical Analysis and Applications, 83(2), 566-569.
  • Khan, M.S., Swaleh, M. and Sessa, S., 1984. Fixed Point Theorems by Altering Distances Between the Points. Bulletin of the Australian Mathematical Society, 30(1), 1-9.
  • Kramosil, O. and Michalek, J., 1975. Fuzzy Metric and Statistical Metric Spaces. Kybernetica, 11, 326-334.
  • Lowen, R., 1976. Fuzzy Topological Spaces and Fuzzy Compactness. Journal of Mathematical Analysis and Applications, 56, 621-633.
  • Mihet, D., 2004. A Banach Contraction Theorem in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 144, 431-439.
  • Nadler, S. B., 1969. Multivalued Contraction Mappings. Pacific Journal of Mathematics, 30(2), 475-488.
  • Naidu, S. V. R., 2003. Some Fixed Point Theorems in Metric Spaces by Altering Distances. Czechoslovak Mathematical Journal, 53(128), 205-212.
  • Nashine H. K. and Aydi, H., 2013. Coupled Fixed Point Theorems for Conctractions Involving Altering Distances in Ordered Metric Spaces. Mathematical Sciences, 7(20), 2013.
  • Pao-Ming, P. and Ying-Ming, L., 1980. Fuzzy Topology: II. Product and Quotient Spaces. Journal of Mathematical Analysis and Applications, 77, 20-37.
  • Phiangsungnoen, S., Sintunavarat, W. and Kumam, P., 2014. Fuzzy Fixed Point Theorems in Hausdorff Fuzzy Metric Spaces. Journal of Inequalities and Applications, 2014(201), 1-10.
  • Popa, V. and Mocanu, M., 2009. Altering Distance and Common Fixed Points Under Implicit Relations. Hacettepe Journal of Mathematics and Statistics, 38(3), 329-337.
  • Rhoades, B. E., 2001. Some Theorems on Weakly Contractive Maps. Nonlinear Analysis: Theory, Methods and Applications, 47(4), 2683-2693.
  • Rodriguez-Lopez, J. and Romaguera, S., 2004. The Hausdorff Fuzzy Metric on Compact Sets. Fuzzy Sets and Systems, 147, 273-283.
  • Schweizer, B. and Sklar, A., 1960. Statistical Metric Spaces. Pacific Journal of Mathematics, 10, 314-334.
  • Shen, Y., Qiu, D., Chen, W., 2012. Fixed Point Theorems in Fuzzy Metric Spaces. Applied Mathematics Letters, 25, 138-141.
  • Türkoğlu, D., Alaca, C., Cho, Y. J., Yıldız, C., 2006. Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Journal of Applied Mathematics and Computing, 22, 411-424.
  • Veeramani, P., 2001. Best Approximation in Fuzzy Metric Spaces. Journal of Fuzzy Mathematics, 9, 75-80.
  • Wong, C. K., 1974. Fuzzy Topology: Product and Quotient Theorems. Journal of Mathematical Analysis and Applications, 45, 512-521.
  • Zadeh, L. A., 1965. Fuzzy Sets. Information and Control, 8, 338-353.
There are 30 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Ferhan Şola Erduran 0000-0002-9433-1016

Publication Date July 15, 2020
Submission Date September 19, 2019
Acceptance Date May 13, 2020
Published in Issue Year 2020 Volume: 10 Issue: 3

Cite

APA Şola Erduran, F. (2020). Sabit Fuzzy Nokta Teoremleri. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(3), 641-650. https://doi.org/10.17714/gumusfenbil.621967