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Strong convergence by a hybrid algorithm for solving equilibrium problem and fixed point problem of a Lipschitz pseudo-contraction in Hilbert spaces. (English) Zbl 06148563
Summary: In this research, we create and prove a strong convergence theorem by using the hybrid iterative algorithm which was proposed by Yao et al. [Nonlinear Anal. 71 (2009) 4997–5002] for finding the common element of fixed point set of a Lipshitz pseudo-contraction and the set of equilibrium problem in Hilbert spaces. Moreover, the results not only cover the original research but can also be applied for finding the common element of the set of zeroes of a Lipshitz monotone mapping and the set of equilibrium problem in Hilbert spaces.

##### MSC:
 47H05 Monotone operators and generalizations 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 47J25 Iterative procedures involving nonlinear operators
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