in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.

This article present a parallel CPU implementation of Kannan algorithm for solving shortest vector problem in Block Korkin-Zolotarev lattice reduction method. Implementation based on Native POSIX Thread Library and show linear decrease of runtime from number of threads.

The existence of coincidence points and common fixed points for operators satisfying a Presić-Kannan type contraction condition in a metric spaces setting is proved. A multi-step iterative method for constructing the common fixed points is also provided.