Modified Halpern’s iteration for fixed point theory of a finite family of G-nonexpansive mappings endowed with graph

Iteration Scheme for Approximating Fixed Points of G-Nonexpansive Maps on Banach Spaces via a Digraph

“…Thereof Lemma 4 (i), 𝑥 𝑛 → 𝑤 * ∈ 𝑔 𝑓𝑖𝑥 . The following two example illustrate which is inspired by Example 2.2 and Example 3.2 in [16] for fulfilling of Theorem 1 − 2 which the Condition (𝐴 ′′ ) and semicompact are used to verify the convergence of iterative algorithm Eq. 1, resp.…”

Some properties of the mapping $T_μ$ introduced by a representation in Banach and locally convex spaces

“…for all t ∈ S and x ∈ C, (5) consider a family of seminorms Q on a locally convex space X which determines the topology of X and a nonempty closed and convex subset C of X. Let G = (V (G), E(G)) be a directed graph such that V (G) = C ( to see more details refer to [4]). A mapping T of C into itself is called Q-G-nonexpansive if q(T x − T y) ≤ q(x − y), whenever (x, y) ∈ E(G) for any x, y ∈ C and q ∈ Q, and a mapping f is a Q-contraction on E if q(f (x) − f (y)) ≤ βq(x − y), for all x, y ∈ E such that 0 ≤ β < 1, (6) consider a family of seminorms Q on a locally convex space X which determines the topology of X.…”

Convergence of CR-iteration to common fixed points of three g-nonexpansive mappings in Banach spaces with graphs

“…In 2018, Kangtunyakarn generalized the results in (Tripak, 2016) to proving Halpern iteration for a finite family of G-nonexpansive mappings in Banach spaces with directed graphs. After that, Suparatulatorn, Cholamjiak, and Suantai generalized the results in (Kangtunyakarn, 2018) and proposed the convergence of S-iteration to some common fixed points of two G-nonexpansive mappings in Banach spaces with directed graphs. In 2018, Sridarat, Suparatulatorn, Suantai, and Cho established the convergence of SPiteration to common fixed points of three G-nonexpansive mappings in uniformly Banach spaces with directed graphs.…”