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Some Fixed Point Theorems in Partial Fuzzy Metric Spaces

Yıl 2020, Cilt: 10 Sayı: 4, 2889 - 2900, 15.12.2020

Başak Aldemir Elif Güner , Ebru Aydoğdu , Halis Aygün

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

Öz

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.

Anahtar Kelimeler

Partial metric partial fuzzy metric completeness fixed point theorem

Kaynakça

  • 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

Yıl 2020, Cilt: 10 Sayı: 4, 2889 - 2900, 15.12.2020

Başak Aldemir Elif Güner , Ebru Aydoğdu , Halis Aygün

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

Öz

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.

Anahtar Kelimeler

completeness partial metric partial fuzzy metric fixed point theorem

Kaynakça

  • 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.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Başak Aldemir Bu kişi benim 0000-0002-9073-9364

Elif Güner 0000-0002-6969-400X

Ebru Aydoğdu 0000-0002-2777-8651

Halis Aygün 0000-0003-3263-3884

Yayımlanma Tarihi 15 Aralık 2020
Gönderilme Tarihi 10 Nisan 2020
Kabul Tarihi 30 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 4

Kaynak Göster

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. Iğdır Üniv. Fen Bil Enst. Der. Aralık 2020;10(4):2889-2900. doi:10.21597/jist.716207
Chicago Aldemir, Başak, Elif Güner, Ebru Aydoğdu, ve Halis Aygün. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology 10, sy. 4 (Aralık 2020): 2889-2900. https://doi.org/10.21597/jist.716207.
EndNote Aldemir B, Güner E, Aydoğdu E, Aygün H (01 Aralık 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, ve H. Aygün, “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 4, ss. 2889–2900, 2020, doi: 10.21597/jist.716207.
ISNAD Aldemir, Başak vd. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology 10/4 (Aralık 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. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:2889–2900.
MLA Aldemir, Başak vd. “Some Fixed Point Theorems in Partial Fuzzy Metric Spaces”. Journal of the Institute of Science and Technology, c. 10, sy. 4, 2020, ss. 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. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(4):2889-900.

Cited By

Soft partial metric spaces
Soft Computing
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A New Approach to Fuzzy Partial Metric Spaces
Hacettepe Journal of Mathematics and Statistics
https://doi.org/10.15672/hujms.1115381