Correction to: Multi-step inertial Krasnosel’skiǐ–Mann iteration with new inertial parameters arrays

1 Correction to: J. Fixed Point Theory Appl. (2021) 23:44 https://doi.org/10.1007/s11784-021-00879-9

In the original publication the equations are wrongly published and this has been corrected in this correction as below;

Under the heading “Introduction”:

a sentence above equation (1.2) should read as “One of the most popular algorithms to solve the fixed point problem (1.1) is the Krasnosel’skiǐ–Mann iteration (shortly, KM iteration) (see, [2,16, 20,24]), which generates $\{x^k\}_{k\in \mathbb {N}}$ given as follows:”

a sentence above equation (1.3) should read as “Recently, the authors [11] introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration (shortly, MiKM iteration) which generates $\{x^k\}_{k\in \mathbb {N}}$ as follows:”

under heading “The MiKM iteration on the affine hull of orbits”: the first sentence should read “Recently, Combettes and Glaudin [5] investigated KM iteration with errors for a countable family of quasi-nonexpansive operators on the affine hull of the orbits, where the operators are not applied to the most current iterate, but to a point in the affine hull of the orbit $\{x^k\}_{k \in \mathbb {N}}$ generated so far.”

Under Theorem 3.1

The last paragraph, should read as “The condition (3.5) seems difficult to verify, since it involves the arrays $\{\mu _{n,k}\}_{n\in \mathbb {N},0\le k\le n}$ and $\{\nu _{n,k}\}_{n\in \mathbb {N},0\le k\le n}$$\{\nu _{n,k}\}_{n\in \mathbb {N},0\le k\le n}$, the sequence $\{\chi _{k}\}_{k \in \mathbb {N}}$ and the iterative sequence $\{x^k\}_{k \in \mathbb {N}}$. However, it can be got rid of when $\{\mu _{n,k}\}_{n\in \mathbb {N},0\le k\le n}$ and $\{\nu _{n,k}\}_{n\in \mathbb {N},0\le k\le n}$ are nonegative”

The original article has been corrected.