A Common Fixed Point Theorem in "Equation missing" -Metric Spaces

Abstract

We give some new definitions of D *-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D *-metric spaces. We get some improved versions of several fixed point theorems in complete D *-metric spaces.

Fixed Point Theorems in S-Metric Spaces

“…Implicit relations on S-metric spaces have been used in many articles (see [3]- [7]). Fixed point theorems for two mappings on complete S-metric spaces will be proved.…”

Unique Common Fixed Points for Generalized Contractive Type Mappings in $D_1$-Space

“…Later, Shaban Sedghi [14] modified the notion of D-metric space and defined the notion of D * -metric spaces. The definition of D * -metric space is stated as follows.…”

“…At the same time Sanodia et al [13] proved a fixed point theorem for single mapping in the G-metric space. Later, someone point out that a D-metric need not be a continuous function of its variables, in order to overcome this problem, Shaban Sedghi [14] modified the notion of D-metric space and defined the notion of D * -metric space in 2007. Then, Aage-Salunke [15] proved that the generalized in D * -metric spaces by replacing the real numbers with an ordered Banach space and defined D * -cone metric spaces and showed the topological properties.…”

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

“…These generalizations were then used to extend the scope of the study of fixed point theory. 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.…”