Advances in Metric Fixed Point Theory and Applications

Abstract

The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: for each n ≥ 1 and showed its convergence with the control conditions αn, βn ϵ [0, 1). In this paper, we present the convergence analysis of the general inertial Krasnosel’skiǐ–Mann algorithm with the control conditions αn ϵ [0, 1], βn ∈ (−∞, 0] and αn ∈ [−1, 0], βn ∈ [0,+∞), respectively. Also, we provide the convergence rate for the general inertial Krasnosel’skiˇı–Mann algorithm under mild conditions on the inertial parameters and some conditions on the relaxation parameters, respectively. Finally, we show that a numerical experiment provided compares the choice of inertial parameters. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021.