In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as well and prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the proven results and enrich the new introduced metric type spaces.2 Partial metric and rectangular metric preliminaries Definition 1.[5] (partial metric space) Let X be a nonempty set. A mapping p : x × X → R + is said to be a partial metric on X if for any x, y, z ∈ X, it satisfies the following conditions: 0 2010 Mathematics Subject Classification: 54E15, 54E50, 47H10 0
In this paper, a new class of functions denoted by
Ψ
ν
is introduced which we use to prove new interesting fixed point results in controlled metric type spaces. Also, we present examples to illustrate our work.
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