Abstract
Abstract The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove some Δ-convergence theorems of the mixed type iteration process to approximating a common fixed point for two asymptotically nonexpansive mappings and two total asymptotically nonexpansive mappings in hyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature. MSC:47H09, 47H10.
Highlights
1 Introduction and preliminaries Most of the problems in various disciplines of science are nonlinear in nature, whereas fixed point theory proposed in the setting of normed linear spaces or Banach spaces majorly depends on the linear structure of the underlying spaces
A nonlinear framework for fixed point theory is a metric space embedded with a ‘convex structure’
Throughout this paper, we work in the setting of hyperbolic spaces introduced by Kohlenbach [ ], defined below, which is more restrictive than the hyperbolic type introduced in [ ] and more general than the concept of hyperbolic space in [ ]
Summary
Introduction and preliminariesMost of the problems in various disciplines of science are nonlinear in nature, whereas fixed point theory proposed in the setting of normed linear spaces or Banach spaces majorly depends on the linear structure of the underlying spaces. A hyperbolic space is uniformly convex [ ] if for any r > and ∈ A mapping T : K → K is said to be asymptotically nonexpansive if there exists a sequence {kn} ⊂ [ , ∞) with kn → such that d Tnx, Tny ≤ ( + kn)d(x, y), ∀n ≥ , x, y ∈ K .
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