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Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

Xiaolong Qin, Yongfu Su, Meijuan Shang (2007)

Open Mathematics

Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: K → E be asymptotically nonexpansive mappings with k n, l n and j n. [1, ∞) such that Σn=1∞(k n − 1) < ∞, Σn=1∞(l n − 1) < ∞ and Σn=1∞(j n − 1) < ∞, respectively and F nonempty, where F = x ∈ K: T 1x = T 2x = T 3 x = xdenotes the common fixed points set of T 1, T 2 and T 3. Let α n, α′ n and α″ n be real sequences in (0, 1) and ∈ ≤ α n, α′ n, α″...

Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm

Lateef O. Jolaoso, Oluwatosin T. Mewomo (2020)

Commentationes Mathematicae Universitatis Carolinae

This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences and also...

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