Fixed point theorems in fuzzy metric spaces

Abstract

We prove a fixed point theorem for mappings satisfying an implicit relation in a complete fuzzy metric space.

A variational approach to a singular elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities

“…1 in (6), we obtain Sðy; y; TyÞ ¼ lim nÀ!1 Sðfx 2n ; fx 2n ; gTx 2nþ1 Þ q maxfSðy; y; TyÞ; 0; 0; Sðy; y; TyÞÞg; that is, again it follows that Ty ¼ y. Also, we can apply condition (1) Since 0\q\1; it follows that Sðfy; fy; yÞ ¼ 0 and fy ¼ y.…”

Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25)

“…It can be easily seen that the following function defines an S-metric on R different from the usual S-metric defined in [15]:…”

“…Recently, Sedghi, Shobe, and Aliouche have defined the concept of an S-metric space as a generalization of a metric space in [14] as follows:…”

“…Definition 1 [14] Let X be a nonempty set, and S : X 3 ! ½0; 1Þ be a function satisfying the following conditions for all x; y; z; a 2 X :…”

Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces

“…For more discussions of such generalizations, we refer to [4,5,6,8,9,13,20]. Sedghi et al [18] have introduced the notion of an S-metric space and proved that this notion is a generalization of a G-metric space and a D * -metric space. Also, they have proved properties of S-metric spaces and some fixed point theorems for a self-map on an S-metric space.…”