[PDF] Top 20 Iterative Algorithm for Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

... Motivated and inspired by the above result, in this paper, we suggest and analyze an it- erative algorithm which has strong convergence. Further, using this result, we consider the convex minimization problem of ... See full document

... of maximal monotone operators is to find an efficient iterative algorithm to compute approximately zeroes of maximal monotone ...of maximal monotone ... See full document

... an iterative algorithm can be developed for the approximation of solu- tions of equation of Hammerstein-type ...approximate solutions of equations of Hammerstein-type using Mann-type (see ...real ... See full document

... η)-maximal monotone operators and discussed the approximation solvability of a new system of nonlinear (set-valued) varia- tional inclusions involving (A, η)-maximal relaxed monotone ... See full document

... the algorithm is often impractical since, in many cases, solving the problem ...of maximal monotone operators is to find an efficient iterative algorithm to compute approximately ... See full document

... a Hilbert space H , let B, G be two set-valued maximal monotone operators on C into H , and let g : H → H be a k-contraction with 0 < k < ...strongly monotone mapping, V : H → H ... See full document

... Many nonlinear problems can be formulated as the problem of finding a zero point of a maximal monotone operator in a Banach space. The proximal point method, which was first introduced by Martinet [] and ... See full document

... algorithm [, ]. If A ≡ , then we obtain the proximal point algorithm [–] and if B ≡ , then we obtain the gradient method []. However, it is noted that the sequences generated by these schemes ... See full document

... the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone operators in Hilbert ... See full document

... of maximal mono- tone operators is to find a zero point of maximal monotone ...for approximating this problem is called the proximal point algorithm introduced by Martinet [] in ... See full document

... the iterative scheme ...a maximal monotone operator and the solution set of the variational inequality problem for an inverse-strongly-monotone operator in a 2-uniformly convex and uniformly ... See full document

... be monotone iff, for all x, y ∈ H, f ∈ Mx and g ∈ My imply x – y, f – g > ...A monotone mapping M : H ⇒ H is maximal iff the graph Graph(M) of R is not properly contained in the graph of any other ... See full document

... This algorithm was first introduced by Martinet 14 and generally studied by Rockafellar 18 in the framework of a Hilbert space ...a Hilbert space H or in a Banach space X; see, for example, 13, 19–23 ... See full document

... An operator T : H → H is said to be nonexpansive if Tx–Ty ≤ x –y for all x, y ∈ H . It is well known that Fix(T ) is closed and convex. It is known that A is called strongly positive if there exists a constant γ >  ... See full document

... In this paper, motivated and inspired by the research going on in this direction, we study the variational inequality (.), and the fixed point and equilibrium problem (.) based on a regularization algorithm. It ... See full document

... an iterative algorithm. Strong convergence of the proposed iterative algorithm has been obtained in the framework of Hilbert ...an iterative algorithm is proposed and ... See full document

... If T satisfies (i) and (ii), then T is called relatively quasi-nonexpansive (see []). In a Hilbert space, relatively quasi-nonexpansive mappings coincide with quasi-nonexpansive map- pings. Quasi-nonexpansive ... See full document

... η-subdifferential operators, maximal η-monotone operators, generalized monotone operators (named H-monotone operators), A-monotone opera- tors, (H ... See full document

... of solutions of a mathematical model related to mixed equilibrium problems and the set of fixed points of a 2-generalized hybrid mapping in a real Hilbert ... See full document

... for maximal monotone operators plays an impor- tant role in ...a Hilbert space, Rockafellar [8] introduced the following iterative ... See full document