Convergence results on Picard-Krasnoselskii hybrid iterative process in CAT(0) spaces

Abstract

We get the strong and Δ\Delta -convergence of the Picard-Krasnoselskii hybrid iteration scheme to a fixed point of a self-map endowed with the condition (Bγ,μ)\left({B}_{\gamma ,\mu }). We use the nonlinear context of CAT(0) spaces for establishing these results. We present a new example of a self-map endowed with (Bγ,μ)\left({B}_{\gamma ,\mu }) condition and prove that its Picard-Krasnoselskii hybrid iterative process is more effective than the Picard and Krasnoselskii hybrid iterative processes. This improves and extends some recently announced results of the current literature.

Keywords

• picard-krasnoselskii hybrid iteration
• fixed point
• (b γ,μ) condition
• delta and strong convergence
• cat(0) spaces
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