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

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

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.

___

  • [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.