id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-5405	M.Sornavalli, R. Selvarani, N. Mehala	Common Neutrosophic Metric Space Fixed Point Theorems with Properties	2025	16	.pdf	application/pdf	7065	296	80	Example: 2.5 [20] Let (Ξ, d) be a Q- metric space, for all 𝜛, 𝜔, 𝜏, 휁 ∈Ξ, and every 휁 > 0, consider 𝒬, ℋ, 𝒪 to be fuzzy sets on Ξ3 x (0, ∞) defined by 𝒬(𝜛, 𝜔, 𝜏, 휁) = 𝜁 𝜁+𝐺(𝜛,𝜔,𝜏,𝜁) and ℋ(𝜛, 𝜛, 𝜔, 휁) = 𝐺(𝜛,𝜔,𝜏,𝜁) 𝜁+𝐺(𝜛,𝜔,𝜏,𝜁) and 𝒪(𝜛, 𝜛, 𝜔, 휁) = 𝐺(𝜛,𝜔,𝜏,𝜁) 𝜁+𝐺(𝜛,𝜔,𝜏,𝜁) denote a∗ b = ab anda ◊ b = min { a+b , 1} . = 1 for all x, y, z ∈ X, t > 0, In this case, the pair (Q, H) is called an intuitionistic generalized fuzzy metric on X. Definition: 2.4 [20] A 6-tuple ( Ξ, 𝒬, ℋ, 𝒪 *, ) is Said to be an Neutrosophic Metric space if Ξ is an arbitrary set, * is a Continuous t-norm, is a Continuous t-conorm, and 𝒬, ℋ, 𝒪 are Neutrosophic set on Ξ2 x (0, ∞) satisfying the following conditions: for all 𝜛, 𝜔, 𝜎 ∈Ξ, 𝜆, 𝜏> 0, (i) 𝒬(𝜛, 𝜔, 𝜏, 휁) + ℋ (𝜛, 𝜔, 𝜏, 휁) + 𝒪 (𝜛, 𝜔, 𝜏, 휁) ≤ 3; (ii) 𝒬(𝜛, 𝜛, 𝜔, 휁) > 0; for 𝜛 ≠ 𝜔; (iii) 𝒬(𝜛, 𝜛𝜔, 휁) ≤ 𝒬(𝜛, 𝜔, 𝜏, 휁), for 𝜔 ≠ 휁; (iv) 𝒬(𝜛, 𝜔, 𝜏, 휁) = 1 if and only if 𝜛 = 𝜔 = 𝜏; (v) 𝒬(𝜛, 𝜔, 𝜏, 휁) * 𝒬(p (𝜛, 𝜔, 𝜏), 휁) where p is a permutation function; (vi) 𝒬(𝜛, a, a, 휁) ∗ 𝒬(𝑎, 𝜔, 𝜏, 휂) ≤ 𝒬(𝜛, 𝜔, 𝜏, 휁 + 휂); (vii) 𝒬(𝜛, 𝜔, 𝜏, .): (0, ∞) → [0,1] is continuous; (viii) 𝒬 is non-decreasing of ℜ+, lim 𝜁→∞ 𝒬(𝜛, 𝜔, 𝜏, 휁) = 1 and lim 𝜁→0 𝒬(𝜛, 𝜔, 𝜏, 휁) = 0 for all 𝜛, 𝜔, 𝜏 ∈Ξ, 휁> 0 (ix) ℋ(𝜛, 𝜛, 𝜔, 휁) < 1; for 𝜛 ≠ 𝜔; (x) ℋ (𝜛, 𝜛𝜔, 휁) ≥ ℋ (𝜛, 𝜔, 𝜏, 휁), for 𝜔 ≠ 휁; (xi) ℋ(𝜛, 𝜔, 𝜏, 휁) = 0	cache/cana-5405.pdf	txt/cana-5405.txt