### A Common Fixed Point of an Infinite Family of Pseudocontractive Maps

#### Abstract

A new inertial algorithm for approximating a common fixed point of an infinite family of strict speudocontractions without any compactness condition on the maps or their domains is constructed. The sequence of the algorithm is proved to converge strongly to a common fixed point of the maps in a uniformly smooth real Banach space. This result is achieved as an application of a new inertial algorithm whose sequence approximates a common zero of an infinite family of inverse strongly accretive maps. In addition, numerical examples are given to compare the efficiency of the sequences of our algorithms over the sequences of some recent algorithms without inertial term. Finally, our theorems improve and complement some recent related results in the literature.

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