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Very recently, Liu [3] considered a general iterative method for equilibrium problems and strict pseudocontractions.
Motivated by [8], Colao et al. [9] introduced an iterative method for equilibrium problem and finite family of nonexpansive mappings (1.9).
In order to obtain convergence of the projection method for equilibrium problems, Tran et al. [5] introduced an extragradient method for pseudomonotone equilibrium problems, which is computationally expensive because of the two projections defined onto the constrained set.
In this paper, a shrinking projection algorithm based on the prediction correction method for equilibrium problems and weak Bregman relatively nonexpansive mappings is introduced and investigated in Banach spaces, and then the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions.
PPB can be calculated using a standard computational method for equilibrium modeling of systems of interacting oligonucleotides (OMP for example) for each probe and target set.
Single sample methods based on linkage disequilibrium (LD), have been proposed (Hill 1981; Waples 2006) and have been compared to the temporal method for equilibrium (i.e. stable population size) scenarios (Waples and Do 2010).
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Iterative methods for equilibrium problems and fixed point problems of nonexpansive mappings have been extensively investigated.
Very recently, Duan and Zhao [10] considered new hybrid methods for equilibrium problems and strict pseudocontractions.
Therefore it is interesting to develop the effective iterative methods for equilibrium problems and fixed point problems of strict pseudo-contractions.
Kim [14] used hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings to prove the strong convergence theorems.
We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space.
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