Fixed point theorems for nonlinear contractions in Kaleva–Seikkala's type fuzzy metric spaces

Some new fixed point theorems in fuzzy metric spaces

“…It can been applied to very different abstract metric spaces and, in particular, very recently, many fixed point results have been obtained in the setting of fuzzy metric spaces (mainly, using George and Veeramani's spaces rather than Kramosil and Michalek's fuzzy metric spaces). See, for instance, [5,20,21,27] and references therein. Recently, Miheţ [17] enlarged the class of Gregori and Sapena's fuzzy contractive mappings (see [10]) and proved a fuzzy Banach contraction result for complete non-Archimedean fuzzy metric spaces in the sense of Kramosil and Michalek.…”

On cyclic (ψ, �)-contractions in Kaleva-Seikkala's type fuzzy metric spaces

“…(2) (R-2) =⇒ for each t ∈ (0, 1] there exists s = s(t) ∈ (0, t] such that [29] ρ t (x, y) ≤ ρ s (x, z) + ρ t (z, y), for all x, y, z ∈ X.…”

“…(see [16]) Let (X, d, L, R) be a FMS with (R-3). Then the family {U(ε, α) : ε > 0, α ∈ (0, 1]} of sets [29]) Let (X, d, L, R) be a FMS with (R-2). Then for each t ∈ (0, 1], ρ t (x, y) is continuous at (x, y) ∈ X × X.…”

Pata-Type Fixed-Point Theorems in Kaleva–Seikkala’s Type Fuzzy Metric Space

“…is result was investigated by many authors from different points of view, see [2][3][4][5][6][7][8][9][10] and the references therein.…”

“…is said to be complete if each Cauchy sequence in X is convergent to some point in X Lemma 4 (see [6]). Let (X, d, L, R) be a fuzzy metric space with (R-2).…”