Approximating common fixed point via Ishikawa's iteration



	Approximating common fixed point via Ishikawa's iteration


	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 G(M) ⊆ M, G(N) ⊆ N, F(M) ⊆ M and (N) ⊆ N; ‖ Fu-Gv ‖ ≤ ‖ u-v ‖ for u ∈ M, v ∈ N; and ‖ 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. Abstract pdf Fulltext pdf Back to volume's table of contents