Find in Library

<p/> <p>The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set <inline-formula> <graphic file="1687-1812-2011-973028-i1.gif"/></inline-formula> of solutions of a generalized equilibrium problem, the set <inline-formula> <graphic file="1687-1812-2011-973028-i2.gif"/></inline-formula> of fixed points of a relatively nonexpansive mapping <inline-formula> <graphic file="1687-1812-2011-973028-i3.gif"/></inline-formula>, and the set <inline-formula> <graphic file="1687-1812-2011-973028-i4.gif"/></inline-formula> of zeros of a maximal monotone operator <inline-formula> <graphic file="1687-1812-2011-973028-i5.gif"/></inline-formula> in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point in <inline-formula> <graphic file="1687-1812-2011-973028-i6.gif"/></inline-formula>. These new results represent the improvement, generalization, and development of the previously known ones in the literature.</p>