Araştırma Makalesi
BibTex RIS Kaynak Göster

Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces

Yıl 2022, Cilt: 5 Sayı: 3, 145 - 151, 23.09.2022
https://doi.org/10.33401/fujma.1034862

Öz

This work introduces a new three-step iteration process and shows that the same leads to a unique fixed point with the help of theorems under different conditions of contractive mappings over-generalized $\mathscr{G}$ - fuzzy metric spaces in the convex structure. Also, we investigate the data dependence result of this iterative process in the generalized $\mathscr{G}$ - fuzzy convex metric spaces.








Kaynakça

  • [1] L. A. Zadeh, Fuzzy sets, Inf. Comput., 8 (1965) 338-353.
  • [2] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kubernetika, 11 (1975), 336-344.
  • [3] A. George, P. Veeramani, On some result in Fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399.
  • [4] Z. Mustafa, B. Sims, A new approach to generalized metric space, J. Nonlinear Convex Anal., 7(2) (2006), 289 - 297.
  • [5] G. Sun, K. Yang, Generalized fuzzy metric spaces with properties, Res. J. App. Sci. Engg. Tech., 2 (2010), 673 - 678.
  • [6] M. Jeyaraman, R. Muthuraj, M. Jeyabharathi, M. Sornavalli, Common fixed point theorems in G -fuzzy metric spaces, J. New Theory, 10 (2016), 12 - 18.
  • [7] K. S. Ha, Y. J. Cho, A. White, Strictly convex and strictly 2-convex 2-normed spaces, Mathematica Japonica, 33(3) (1988), 375-384.
  • [8] M. Jeyaraman, V. Vinoba, V. Pazhani, Convex structure in generalized Fuzzy metric spaces, Eur. J. Math. Stat., 2(4), 13-16, https://doi.org/10.24018/ejmath.2021.2.4.27.
  • [9] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779.
  • [10] A. Rafik, Fixed points of ciric quasi-contractive operators in generalized convex metric spaces, Gen. Math., 14(3) (2006), 79-90.
  • [11] W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142-149.
  • [12] P. Thangavelu, S. Shyamala Malini, P. Jeyanthi, Convexity in D-Metric Spaces and its applications to fixed point theorems, Int. J. Stat. Math., 2(3) (2012), 5-12.
  • [13] X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proc. Am. Math. Soc., 113 (1991), 727-731.
Yıl 2022, Cilt: 5 Sayı: 3, 145 - 151, 23.09.2022
https://doi.org/10.33401/fujma.1034862

Öz

Kaynakça

  • [1] L. A. Zadeh, Fuzzy sets, Inf. Comput., 8 (1965) 338-353.
  • [2] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kubernetika, 11 (1975), 336-344.
  • [3] A. George, P. Veeramani, On some result in Fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399.
  • [4] Z. Mustafa, B. Sims, A new approach to generalized metric space, J. Nonlinear Convex Anal., 7(2) (2006), 289 - 297.
  • [5] G. Sun, K. Yang, Generalized fuzzy metric spaces with properties, Res. J. App. Sci. Engg. Tech., 2 (2010), 673 - 678.
  • [6] M. Jeyaraman, R. Muthuraj, M. Jeyabharathi, M. Sornavalli, Common fixed point theorems in G -fuzzy metric spaces, J. New Theory, 10 (2016), 12 - 18.
  • [7] K. S. Ha, Y. J. Cho, A. White, Strictly convex and strictly 2-convex 2-normed spaces, Mathematica Japonica, 33(3) (1988), 375-384.
  • [8] M. Jeyaraman, V. Vinoba, V. Pazhani, Convex structure in generalized Fuzzy metric spaces, Eur. J. Math. Stat., 2(4), 13-16, https://doi.org/10.24018/ejmath.2021.2.4.27.
  • [9] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771-779.
  • [10] A. Rafik, Fixed points of ciric quasi-contractive operators in generalized convex metric spaces, Gen. Math., 14(3) (2006), 79-90.
  • [11] W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142-149.
  • [12] P. Thangavelu, S. Shyamala Malini, P. Jeyanthi, Convexity in D-Metric Spaces and its applications to fixed point theorems, Int. J. Stat. Math., 2(3) (2012), 5-12.
  • [13] X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proc. Am. Math. Soc., 113 (1991), 727-731.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Pazhanı V 0000-0002-4586-9354

M. Jeyaraman 0000-0002-0364-1845

Yayımlanma Tarihi 23 Eylül 2022
Gönderilme Tarihi 9 Aralık 2021
Kabul Tarihi 26 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA V, P., & Jeyaraman, M. (2022). Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces. Fundamental Journal of Mathematics and Applications, 5(3), 145-151. https://doi.org/10.33401/fujma.1034862
AMA V P, Jeyaraman M. Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces. FUJMA. Eylül 2022;5(3):145-151. doi:10.33401/fujma.1034862
Chicago V, Pazhanı, ve M. Jeyaraman. “Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces”. Fundamental Journal of Mathematics and Applications 5, sy. 3 (Eylül 2022): 145-51. https://doi.org/10.33401/fujma.1034862.
EndNote V P, Jeyaraman M (01 Eylül 2022) Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces. Fundamental Journal of Mathematics and Applications 5 3 145–151.
IEEE P. V ve M. Jeyaraman, “Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces”, FUJMA, c. 5, sy. 3, ss. 145–151, 2022, doi: 10.33401/fujma.1034862.
ISNAD V, Pazhanı - Jeyaraman, M. “Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces”. Fundamental Journal of Mathematics and Applications 5/3 (Eylül 2022), 145-151. https://doi.org/10.33401/fujma.1034862.
JAMA V P, Jeyaraman M. Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces. FUJMA. 2022;5:145–151.
MLA V, Pazhanı ve M. Jeyaraman. “Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 3, 2022, ss. 145-51, doi:10.33401/fujma.1034862.
Vancouver V P, Jeyaraman M. Fixed Point Theorems in $\mathscr{G}$ - Fuzzy Convex Metric Spaces. FUJMA. 2022;5(3):145-51.

Creative Commons License
The published articles in Fundamental Journal of Mathematics and Applications are licensed under a