Abstract
In this paper, we prove strong and weak convergence results of modified Ishikawa iterative process to common fixed points of two nearly lipschitzian mappings in the framework of hyperbolic spaces.Our results extend and improve results of (4) and (11) from uniformly convex Banach spaces and CAT (0) spaces to hyperbolic spaces.
Highlights
Hyperbolic space is an important example of the geodesic space
Fixed point theory of non-linear mappings in the set up of hyperbolic space is a fascinating field of research.Hyperbolic space is inherit rich geometrical structure
Its structural properties play a key role in obtaining new results in metric fixed point theory.Our aim is to prove strong and weak convergence results of modified Ishikawa iterative process to common fixed points of two nearly lipschitzian mappings in the framework of hyperbolic space defined by Kohlenbach [5] which is: A metric space (X, d) is a hyperbolic space if there exists a map W : X × X × [0, 1] → X satisfying: 1. d(u, W (x, y, α)) ≤ αd(u, x) + (1 − α)d(u, y), 2. d(W (x, y, α), W (x, y, β)) = |α − β|d(x, y), 3
Summary
Let H be a non-empty compact convex subset of a hyperbolic space X and let t, T : H → H be two uniformly continuous and nearly lipschitzian mappings with sequences {a′n, η1(tn)} and {a′n′ , η2(T n)} respectively such that Σ∞ n=1 a′n < ∞,Σ∞ n=1a′n′ < ∞ and F (t) F (T ) = φ.
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