On Some Fixed Curves in Metric Spaces

Some New Fixed Point Theorems in Fuzzy Metric Spaces

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

Some remarks about curves in metric spaces

and when this happens we say that d(x, y) is an ultrametric. One can check that an ultrametric space is totally disconnected, which is to say that it does not contain a connected subset with more than two elements. Let us say that a subset E of a metric space (M, d(x, y)) is chain connected if for every pair of points u, v ∈ E and every ǫ > 0 there is a finite chain w1, . . . , wl of points in ...

Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...

Some Coupled Fixed Point Results on Partial Metric Spaces

Some Fixed Point Theorems on Ordered Metric Spaces and Application

Existence of fixed points in partially ordered sets has been considered recently in 1 , and some generalizations of the result of 1 are given in 2–6 . Also, in 1 some applications to matrix equations are presented, in 3, 4 some applications to periodic boundary value problem and to some particular problems are, respectively, given. Later, in 6 O’Regan and Petruşel gave some existence results fo...