Subordinate Semimetric Spaces and Fixed Point Theorems

Abstract EN

We introduce the concept of subordinate semimetric space.

Such notion includes the concept of RS-space introduced by Roldán and Shahzad; therefore the concepts of Branciari’s generalized metric space and Jleli and Samet’s generalized metric space are particular cases.

For such spaces we prove a version of Matkowski’s fixed point theorem, and introducing the concept of q-contraction we get a fixed point theorem of Kannan-Ćirić type.

Moreover, using such result we characterize complete subordinate semimetric spaces.