On Fuzzy Soft G-Metric Spaces

Some New Results of Fixed Point in Fuzzy Soft G-metric Spaces

“…Taking the limit as n → ∞ from which, we see that (ā−2b)G(f e , T h en , T h en ) →0 and so, by proposition (4.1) in [2] we have that the sequence {T h en } n∈N is fuzzy soft G-convergent to T f e = f e , therefore proposition (4.4) in [2] implies that T is fuzzy soft G-continuous at f e . Theorem 3.…”

“…Note that, (Ẽ,G) is a symmetric fuzzy soft G-metric(Proposition 3.3, [2]). Now, we show that (Ẽ,G) is fuzzy soft G-complete.…”

“…Case (2): If min G (g e n+1 , g e n+2 , , g e n+2 ), G(g en , g e n+1 , T g e n+1 ) =G(g en , g e n+1 , g e n+1 ), then aG(g e n+1 , g e n+2 , g e n+2 ) +bG(g en , g e n+1 , g e n+1 )≤cG(g en , g e n+1 , g e n+1 )…”

“…Definition 6. [2] Let (Ẽ,G) be a fuzzy soft G-metric space and {f en } be sequence of fuzzy soft elements inẼ. Then the sequence {f en } is said to be fuzzy soft G-Cauchy if for everỹ ≥0 , there existδ>0 and a positive integer N = N (˜ ) such thatG(f en , f em , f e l )<˜ for all n, m, l ≥ N ; that isG(f en , f em , f e l ) →0 as n, m, l → ∞.…”

“…Güler and Yildirim presented soft G-Cauchy sequences and soft G-complete metric spaces in [10], and Shrivastava et al established fixed point results of mapping defined on soft G-metric spaces in [17]. Using fuzzy soft elements, Sayed et al proposed the concept of fuzzy soft G-metric space in [2]. They also investigated on fuzzy soft continuity and convergence in fuzzy soft G-metric spaces.…”