On some common fixed point results for two infinite families of uniformly L-Lipschitzian total asymptotically quasi-nonexpansive mappings

Abstract

Abstract In this manuscript, we introduce a new class of uniformly L-Lipschitzian and total asymptotically quasi-nonexpansive mappings, which is significantly more general than many known nonexpansive mappings that appeared before. We establish some convergence and Δ-convergence theorems for two infinite families of such mappings in the setting of CAT(κ) spaces. Our results refine, generalize, and improve several corresponding results in the existing literature.

Keywords

• Common fixed point
• Δ-Convergence
• Asymptotically quasi-nonexpansive map
• Total asymptotically nonexpansive mappings
• CAT(0) space
• Hyperbolic space