Convex contractions on extended b-metric spaces

Abstract

This research investigated different types of convex contractions in the setting of extended $ b $-metric spaces from the point of view of the existence and uniqueness of their fixed points. The assumptions imposed on involved mappings refer to convexity of order $ 2 $, two-sided convexity or Ćirić-type convexity, which also fulfill a continuity type condition. An example was provided to emphasize the usability of the results.

Keywords

• extended $ b $-metric space
• generalized metric space
• convex contraction
• generalized contraction