Common Fixed Point of Two R-Weakly Commuting Mappings in Sb-Metric Spaces

Minimal Sets with Maximum Cardinality

“…Unlike in the theory of G-metric space, where condition (D1) was replaced with the three separate axioms (G1), (G2), and (G3), Sedghi et al [27] observed that condition (D1) can be replaced with two axioms and thus introduced the notion of a * -metric space as follows. Note that condition (D1) has been replaced with ( * 1) and ( * 2).…”

“…Mustafa and Sims [22] introduced a new structure of generalized metric spaces which are called G-metric spaces as a generalization of metric spaces ( , ) to develop and introduce a new fixed point theory for various mappings in this new structure. Sedghi et al [27] have introduced * -metric spaces which is a probable modification of the definition of D-metric spaces introduced by Dhage [7] and proved some basic properties in * -metric spaces, (see [27,29]). …”

Fixed points of (α,ψ,φ)-generalized weakly contractive maps and property(P) in S-metric spaces

“…For more works on the existence of fixed points in G-metric spaces we refer Babu, Babu, Rao and Kumar [5], Chugh, Kadian Anju and Rhoades [8] and Mustafa, Obiedat, Awawdeh [18] and the related references cited in these papers. In 2007, Sedghi [21] introduced D*-metric spaces which is a probable modification of the definition of D-metric spaces introduced by Dhage [9] and proved some basic properties of D*-metric spaces [20,21]. In 2012, Sedghi, Shobe and Aliouche [22] introduced a new concept on metric spaces, namely S-metric spaces and studied some properties of these spaces.…”

Best proximity point results in S-metric spaces

“…Later, a number of authors have proved so many fixed point results on the setting of G-metric spaces (see [1], [3] [4], [12], [19], [20], [21], [23]). In [28], Sedghi et al introduced a D * -metric space which is a modification of D-metric spaces introduced by Dhage [8] and proved some basic properties in D * -metric spaces, (see [27], [28]). We note that every G-metric is a D * -metric, but in general the converse is not true, (see Example 1.4 in [29], for example).…”