A note on cone metric fixed point theory and its equivalence

Fixed point results in generalized metric spaces without Hausdorff property

“…However, later it became clear that a lot of these results can be reduced to their standard metric counterparts using various methods. These include, among others, the so-called scalarization method [38] and the method of Minkowski functional [39]. Generalized cone metric spaces and fixed point results in them were treated in [6,21,22,31].…”

Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results

“…(ii) In 2012,Ćirić et al [10] show that the method of Du [13] for contraction mappings in cone metric spaces cannot be applied for contraction mappings in cone metric spaces with a associated c-distance. Also, their notes are hold for generalized c-distance in cone b-metric spaces.…”

Two Fixed Point Theorems in Topological vector space Valued Cone Metric Spaces with Complete Topological Algebra Cones

“…In 2009 I.Beg et al [3] and in 2010 Du [5] generalized cone metric spaces to topological vector space valued cone metric spaces (TVS-CMS). In this approach ordered topological vector spaces are used as the codomain of the metric, instead of Banach spaces.…”

“…See [2], [3] and [5]. One of the tools used to prove such equivalences is the so called nonlinear scalarization function.…”

“…This method was used earlier in optimization theory to convert optimization problems in vectorial forms to their scalar forms. This function was introduced into fixed point theory by Du [5].…”