Abstract We correct a logic mistake in our paper “On statistical convergence and strong Cesàro by moduli” (León-Saavedra et al. J. Inequal. Appl. 23:298, 2019).

in this paper, we shall define and study the concept of  -statistical convergence and  -statistical cauchy inrandom 2-normed space. we also introduce the concept of  -statistical completeness which would provide amore general frame work to study the completeness in random 2-normed space. furthermore, we also prove some new results.

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...