Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 12, Number 2 (2016), pp. 1753–1765 © Research India Publications http://www.ripublication.com/gjpam.htm Kannan - Type Fixed Point Theorem for Four Maps in Cone Pentagonal Metric Spaces Abba Auwalu Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10, Turkey. Evren Hınçal Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10, Turkey. Abstract In this paper, we prove Kannan - type fixed point theorem for four self mappings in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by many authors. AMS subject classification: 47H10, 54H25. Keywords: Cone pentagonal metric spaces, Common fixed point, Contraction map- ping principle, Weakly compatible maps. 1. Introduction Let (X, d) be a metric space and S : X → X be a mapping. Then S is called Kannan contraction if there exists α ∈[0, 1/2) such that d(Sx,Sy) ≤ α  d(x,Sx) + d(y,Sy)  , for all x,y ∈ X. (1) Kannan [10] proved that if X is complete, then every Kannan contraction has a fixed point.