# A new iterative method based on the modified proximal-point algorithm for finding a common null point of an infinite family of accretive operators in Banach spaces

### Abstract

In this paper, we introduce and study a new iterative method for finding a common null point of an infinite family of accretive operators with a strongly accretive and Lipschitzian operator, by using the proximal-point algorithm. And also we prove that the common null point is a unique solution of variational inequality without imposing any compactness-type condition on either the operators or the space considered. Finally, some applications of the main results to equilibrium problems and fixed point problems with an infinite family of pseudocontractive mappings are given. The main result is a generalization and improvement of numerous well-known results in the available literature.

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*CUBO*, vol. 22, no. 2, pp. 155–175, Aug. 2020.

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