# An algorithm for equilibrium problems with mixed-type fixed point constraints

## TL;DR

This paper introduces a new algorithm for solving equilibrium problems with specific fixed point constraints in a mathematical space.

## Contribution

The paper introduces a novel class of nonlinear mappings and a new method for solving equilibrium problems.

## Key findings

- The new method converges strongly to the solution set of an equilibrium problem.
- The method also converges to the set of common fixed points of two families of mappings.
- A numerical example demonstrates the method's implementability.

## Abstract

In this paper, we introduce a novel class of nonlinear mappings known as ϑ-strictly asymptotically pseudocontractive-type multivalued mapping (ϑ-SAPM) in a Hilbert space domain. In addition, a new method was initiated, and it was shown that this method converges strongly to the solution set of an equilibrium problem (EP) and the set of common fixed points of two finite families of type-one (ϑ-SAPM) and ϑ-strictly pseudocontractive-type multivalued mapping (ϑ-SPM). Moreover, we showed that the classes of mappings considered are independent and also presented a numerical example to illustrate the implementablity of the suggested method. The results obtained improve, generalize and extend several conclusions reported in literature.