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Section 3 devises the acceleration algorithm for solving fixed point problems and presents its convergence analysis.
This section is devoted to solving fixed point problems in unbounded sets.
Namely, Cauchy, Liouville, Lipschitz, Peano, Fredholm, Picard, Banach, Browder, Helpern, Mann, Ishikawa, etc., have given different kinds of iterative methods for solving fixed point problems.
Related iterative methods for solving fixed point problems, variational inequalities and optimization problems can be found in [10 15] and the references therein.
It is worth pointing out that, related iterative methods for solving fixed point problems, variational inequalities and optimization problems can be found in [19 35].
As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces.
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This aligns directly with first order problem solving (fixing and forgetting), to the exclusion of second order problem solving (fixing and reporting).
At a cognitive level, Tucker and Edmondson 27 29 studied healthcare practitioners' first order problem solving (fixing the problem at hand) and second order problem solving (understanding why the problem exists, aiming to correct the drivers, and thereby enhancing organisational learning).
Hence, Q s has a unique fixed point in C, denoted by x s, t s, which uniquely solves fixed point equation (7).
Several authors considered some approaches to solve fixed point problems, optimization problems, variational inequality problems and equilibrium problems; see, for example, [2 32] and the references therein.
Subsequently, many authors (see, e.g.[15 19] and references therein) have used the hybrid methods to solve fixed point problems and equilibrium problems.
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