In this paper, we introduce the concepts of partial-quasi k-metric spaces and strongly partial- quasi spaces, their relationship to metric are studied. Furthermore, obtain some results on fixed point theorems in spaces.

Frame theory is an active research area in mathematics, computer science and engineering with many exciting applications a variety of different fields. In this paper we study the notion dual continuous K-frames Hilbert spaces. Also establish some properties.

We extend some known fixed point results for mappings satisfying Kannan type conditions to the context of K-metric spaces. Firstly, we prove a common fixed point result for noncommuting maps. A generalization of Kannan’s fixed point theorem is given in some class of spaces including K-metric spaces.