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Some Fixed Point Theorems in Partial Fuzzy Metric Spaces

Year 2020, Volume: 10 Issue: 4, 2889 - 2900, 15.12.2020

Başak Aldemir Elif Güner Ebru Aydoğdu Halis Aygün

https://doi.org/10.21597/jist.716207
Cited By: 2

Abstract

The aim of this study is basically to give some fundamental fixed point theorems in partial fuzzy metric spaces. Firstly, we investigate the relationships of partial metric space and fuzzy metric space with partial fuzzy metric spaces. Then we define some contractive/contraction mappings similar to the Banach contraction mappings in the classical sense. Also, we show that these mappings have a unique fixed point under some conditions. Finally, we give some examples to illustrate the validity of the obtained results and the necessity of added conditions.

Keywords

Partial metric partial fuzzy metric completeness fixed point theorem

References

  • Altun I, Sola F, Simsek H, 2010. Generalized contractions on partial metric spaces. Topology and its Applications, 157(18):2778-2785.
  • Başarır M, Şahin A, 2017. Some results of the new iterative scheme in hyperbolic space. Communications of the Korean Mathematical Society, 32(4):1009-1024.
  • Bukatin M, Kopperman R, Matthews S, Pajoohesh H, 2009. Partial Metric Space. The American Mathematical Monthly, 116(8):708-718.
  • Czerwik S, 1993. Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1):5-11.
  • Gäher S, 1963. 2-metriche raume and ihre topologische structur. Mathematische Nachrichten, 26:115-148.
  • George A, Veeramani P, 1994. On Some Results in Fuzzy Metric Space. Fuzzy Sets and Systems, 90:365-368
  • Gregori V, Miñana JJ, Miravet D, 2019. Fuzzy partial metric spaces. International Journal of General Systems, 48(3):260-279.
  • Gregori V, Morillas S, Sapena A, 2010. On a class of completable fuzzy metric spaces. Fuzzy Sets and Systems 161(16):2193-2205.
  • Gregori V, Sapena A, 2002. On fixed point theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 125:245-252.
  • Grabiec M, 1988. Fixed point in fuzzy metric space. Fuzzy Sets and Systems, 27(3):385-389.
  • Haghi RH, Rezapour S, Shahzad N, 2013. Be careful on partial metric fixed point results. Topology and its Applications, 160(3): 450-454.
  • Kramosil I, Michalek J, 1975. Fuzzy metrics and statistical metric space. Kybernetica, 11(5):336-344.
  • Kaleva O, Seikkala S, 1984. On fuzzy metric space. Fuzzy Sets and Systems, 12(3):215-229.
  • Lahiri BK, Das P, Dey LK, 2011. Cantor’s theorem in 2-metric spaces and its applications to fixed point problems. Taiwanese Journal of Mathematics, 15(1):337-352.
  • Matthews S, 1994. Partial Metric Topology. Annals of the New York Academy of Sciences-Paper Edition, 728:183-197.
  • Mihet D, 2004. A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets and Systems, 144(3):431-439.
  • Mihet D, 2008. Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems, 159(6):739-744.
  • Mustafa Z, Sims B, 2006. A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7(2): 289-297.
  • O’Neill SJ, 1996. Partial metrics, valuations and domain theory. Annals of the New York Academy of Sciences, 806(1):304-315.
  • Piera AS, 2001. A contribution to the study of fuzzy metric spaces. Applied General Topology, 2(1):63-75.
  • Rodriguez-Lopez J, Romaguera S, 2004. The Hausdorff fuzzy metric on compact sets. Fuzzy Sets and Systems, 147(2):273-283.
  • Sedghi S, Shobkolaei N, Altun I, 2015. Partial fuzzy metric space and some fixed point results. Communications in Mathematics, 23(2):131-142.
  • Şahin A, Başarır M, Khan SH, 2015. On the g-best proximity point results for G-generalized proximal contraction mappings in G-metric spaces. AIP Coference Proocedings, 1676, 020025.
  • Valero O, 2005. On Banach fixed point theorems for partial metric spaces. Applied General Topology, 6(2):229-240.
  • Vasuki R, Veeramani P, 2003. Fixed Point Theorems and Cauchy Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 135(3):415-417.
  • Yue Y, Gu M, 2014. Fuzzy partial (pseudo-)metric space. Journal of Intelligent and Fuzzy Systems, 27(3):1153-1159.
  • Zadeh, LA, 1965. Fuzzy sets. Information and Control, 8(3):338-353.

Some Fixed Point Theorems in Partial Fuzzy Metric Spaces

Year 2020, Volume: 10 Issue: 4, 2889 - 2900, 15.12.2020

Başak Aldemir Elif Güner Ebru Aydoğdu Halis Aygün

https://doi.org/10.21597/jist.716207
Cited By: 2

Abstract

The aim of this study is basically to give some fundamental fixed point theorems in partial fuzzy metric spaces. Firstly, we investigate the relationships of partial metric space and fuzzy metric space with partial fuzzy metric spaces. Then we define some contractive/contraction mappings similar to the Banach contraction mappings in the classical sense. Also, we show that these mappings have a unique fixed point under some conditions. Finally, we give some examples to illustrate the validity of the obtained results and the necessity of added conditions.

Keywords

completeness partial metric partial fuzzy metric fixed point theorem

References

  • Altun I, Sola F, Simsek H, 2010. Generalized contractions on partial metric spaces. Topology and its Applications, 157(18):2778-2785.
  • Başarır M, Şahin A, 2017. Some results of the new iterative scheme in hyperbolic space. Communications of the Korean Mathematical Society, 32(4):1009-1024.
  • Bukatin M, Kopperman R, Matthews S, Pajoohesh H, 2009. Partial Metric Space. The American Mathematical Monthly, 116(8):708-718.
  • Czerwik S, 1993. Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1):5-11.
  • Gäher S, 1963. 2-metriche raume and ihre topologische structur. Mathematische Nachrichten, 26:115-148.
  • George A, Veeramani P, 1994. On Some Results in Fuzzy Metric Space. Fuzzy Sets and Systems, 90:365-368
  • Gregori V, Miñana JJ, Miravet D, 2019. Fuzzy partial metric spaces. International Journal of General Systems, 48(3):260-279.
  • Gregori V, Morillas S, Sapena A, 2010. On a class of completable fuzzy metric spaces. Fuzzy Sets and Systems 161(16):2193-2205.
  • Gregori V, Sapena A, 2002. On fixed point theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 125:245-252.
  • Grabiec M, 1988. Fixed point in fuzzy metric space. Fuzzy Sets and Systems, 27(3):385-389.
  • Haghi RH, Rezapour S, Shahzad N, 2013. Be careful on partial metric fixed point results. Topology and its Applications, 160(3): 450-454.
  • Kramosil I, Michalek J, 1975. Fuzzy metrics and statistical metric space. Kybernetica, 11(5):336-344.
  • Kaleva O, Seikkala S, 1984. On fuzzy metric space. Fuzzy Sets and Systems, 12(3):215-229.
  • Lahiri BK, Das P, Dey LK, 2011. Cantor’s theorem in 2-metric spaces and its applications to fixed point problems. Taiwanese Journal of Mathematics, 15(1):337-352.
  • Matthews S, 1994. Partial Metric Topology. Annals of the New York Academy of Sciences-Paper Edition, 728:183-197.
  • Mihet D, 2004. A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets and Systems, 144(3):431-439.
  • Mihet D, 2008. Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems, 159(6):739-744.
  • Mustafa Z, Sims B, 2006. A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7(2): 289-297.
  • O’Neill SJ, 1996. Partial metrics, valuations and domain theory. Annals of the New York Academy of Sciences, 806(1):304-315.
  • Piera AS, 2001. A contribution to the study of fuzzy metric spaces. Applied General Topology, 2(1):63-75.
  • Rodriguez-Lopez J, Romaguera S, 2004. The Hausdorff fuzzy metric on compact sets. Fuzzy Sets and Systems, 147(2):273-283.
  • Sedghi S, Shobkolaei N, Altun I, 2015. Partial fuzzy metric space and some fixed point results. Communications in Mathematics, 23(2):131-142.
  • Şahin A, Başarır M, Khan SH, 2015. On the g-best proximity point results for G-generalized proximal contraction mappings in G-metric spaces. AIP Coference Proocedings, 1676, 020025.
  • Valero O, 2005. On Banach fixed point theorems for partial metric spaces. Applied General Topology, 6(2):229-240.
  • Vasuki R, Veeramani P, 2003. Fixed Point Theorems and Cauchy Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 135(3):415-417.
  • Yue Y, Gu M, 2014. Fuzzy partial (pseudo-)metric space. Journal of Intelligent and Fuzzy Systems, 27(3):1153-1159.
  • Zadeh, LA, 1965. Fuzzy sets. Information and Control, 8(3):338-353.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Başak Aldemir This is me 0000-0002-9073-9364

Elif Güner 0000-0002-6969-400X

Ebru Aydoğdu 0000-0002-2777-8651

Halis Aygün 0000-0003-3263-3884

Publication Date December 15, 2020
Submission Date April 10, 2020
Acceptance Date July 30, 2020
Published in Issue Year 2020 Volume: 10 Issue: 4

Cite

APA Aldemir, B., Güner, E., Aydoğdu, E., Aygün, H. (2020). Some Fixed Point Theorems in Partial Fuzzy Metric Spaces. Journal of the Institute of Science and Technology, 10(4), 2889-2900. https://doi.org/10.21597/jist.716207
AMA Aldemir B, Güner E, Aydoğdu E, Aygün H. Some Fixed Point Theorems in Partial Fuzzy Metric Spaces. J. Inst. Sci. and Tech. December 2020;10(4):2889-2900. doi:10.21597/jist.716207
Chicago Aldemir, Başak, Elif Güner, Ebru Aydoğdu, and Halis Aygün. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology 10, no. 4 (December 2020): 2889-2900. https://doi.org/10.21597/jist.716207.
EndNote Aldemir B, Güner E, Aydoğdu E, Aygün H (December 1, 2020) Some Fixed Point Theorems in Partial Fuzzy Metric Spaces. Journal of the Institute of Science and Technology 10 4 2889–2900.
IEEE B. Aldemir, E. Güner, E. Aydoğdu, and H. Aygün, “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”, J. Inst. Sci. and Tech., vol. 10, no. 4, pp. 2889–2900, 2020, doi: 10.21597/jist.716207.
ISNAD Aldemir, Başak et al. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology 10/4 (December 2020), 2889-2900. https://doi.org/10.21597/jist.716207.
JAMA Aldemir B, Güner E, Aydoğdu E, Aygün H. Some Fixed Point Theorems in Partial Fuzzy Metric Spaces. J. Inst. Sci. and Tech. 2020;10:2889–2900.
MLA Aldemir, Başak et al. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology, vol. 10, no. 4, 2020, pp. 2889-00, doi:10.21597/jist.716207.
Vancouver Aldemir B, Güner E, Aydoğdu E, Aygün H. Some Fixed Point Theorems in Partial Fuzzy Metric Spaces. J. Inst. Sci. and Tech. 2020;10(4):2889-900.

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