Publication

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.