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

Abstract

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 ( B γ , 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 ( B γ , 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.