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In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2−uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.

mathematical modelling and analysis/mathematical modeling and analysis

PROXIMAL POINT ALGORITHM FOR A COMMON OF COUNTABLE FAMILIES OF INVERSE STRONGLY ACCRETIVE OPERATORS AND NONEXPANSIVE MAPPINGS WITH CONVERGENCE ANALYSIS