Indian Journal of Industrial and Applied Mathematics
  • Year: 2019
  • Volume: 10
  • Issue: 1SI

A New Iterative Class for Finding Common Fixed Points of a Finite Family of Generalized Total Asymptotically Nonexpansive and Multivalued Mappings in Hyperbolic Spaces

1Department of Applied Mathematics, Z H College of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India

*(Corresponding author) Email: s_husain68@yahoo.com

**nishasingh096@gmail.com

Abstract

The purpose of the paper is to introduce a general iteration process for the finite families of total asymptotically nonexpansive mappings and generalized nonexpansive multivalued map- pings in hyperbolic space which include Hadamard manifold and CAT(0) space as special cases. Some important properties of the new defined iterative process are analyzed. Finally, Δ- conver-gence and strong convergence for the iterative process in hyperbolic space are established. The results presented in this paper extend and improve some existing results.

Keywords

common fixed point, asymptotically nonexpansive mapping, strong convergence, Δ-convergence, hyperbolic space, 47H10, 47H09, 49M05, 54E70