Afr. Mat. DOI 10.1007/s13370-016-0467-3 A note on partial metric type structures and metric type structures Maggie Aphane 1 · Seithuti Moshokoa 1 Received: 29 April 2016 / Accepted: 14 October 2016 © African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016 Abstract In the note we discuss partial metric type structures and present their basic prop- erties as well as their relationship with metric type structures. As an application, fixed point theorems for a Lipschitzian map on this structures will be presented. Keywords Partial metric space · Partial cone metric space · Cauchy complete · 0-Cauchy complete Mathematics Subject Classification 54A05 · 40A05 · 47H10 1 Basic notions and preliminaries In the sequel the letter N will denote the set of positive integers. In this section we recall some well known notions, definitions and results that will be used through out the paper. A subset P of a real Banach space E is called a cone if, (i) P is closed, nonempty and P  ={0}; (ii) if for a, b ∈ R, a, b ≥ 0 and x , y ∈ P, then ax + by ∈ P ; (iii) if for both a ∈ P and −a ∈ P, then a = 0. Given a cone P in E a partial ordering ≤ on E via P is defined by a ≤ b if and only if b − a ∈ P for a, b ∈ E . We write a < b to indicate that a ≤ b but a  = b while a << b will stand for b − a ∈ int ( P ), where int ( P ), denotes the interior of P in the norm topology of E . The cone P in E is called normal if there exists a constant M > 0 such that for all a, b ∈ E , 0 ≤ a ≤ b implies ||a|| ≤ M||b||. B Seithuti Moshokoa MoshokoaSP@tut.ac.za Maggie Aphane AphaneM@tut.ac.za 1 Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa 123