Vol. 22(2021) No. 2



  Approximating common fixed point via Ishikawa's iteration
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Fixed Point Theory, Volume 22, No. 2, 2021, 645-662, July 1st, 2021

DOI: 10.24193/fpt-ro.2021.2.42

Authors: R. Gopi and V. Pragadeeswarar

Abstract: In this work, we approximate a common fixed point of mappings F, G : M ∪ N → M ∪ N, satisfying the conditions

  1. G(M) ⊆ M, G(N) ⊆ N, F(M) ⊆ M and (N) ⊆ N;
  2. ‖ Fu-Gv ‖ ≤ ‖ u-v ‖ for u ∈ M, v ∈ N; and
  3. ‖ Fu-Gv ‖ ≤ ‖ u-v ‖ for u ∈ N, v ∈ M,
where M and N are nonempty bounded closed convex subsets of a uniformly convex Banach space. We consider Ishikawa iteration associated with F and G and von Neumann sequence associated with Ishikawa iteration to approximate the common fixed point of F and G. We prove convergent results for common fixed point of F and G. Finally, we give corollaries on common best proximity point for cyclic mappings.

Key Words and Phrases: Nonexpansive mappings, best proximity points, fixed points, Banach space, Von Neumann sequences.

2010 Mathematics Subject Classification: 47H10, 46B20, 54H25.

Published on-line: July 1st, 2021.

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