... and X. Qin, “A new iterative method for solving equilibrium problems and fixedpoint problems for in nite family of nonexpansive mappings,” Fixed Point Theory and Applications,vol. 2010, Article ... the equilibrium problems in Hilbert spaces or Banachspaces; see, for example, 11–25 .In 20, Qin et al. considered the following iterative scheme by a hybrid method in a Banach space:x0∈ ... quasi-φ-nonexpansive mapping for each i ∈{1, 2, ,N},αn,0, {αn,1}, ,{αn,N} are real sequences in 0, 1 satisfyingNj0αn,j 1 for each n ≥ 1andlim infn →∞αn,0αn,i> 0 for each i ∈{1,...