[PDF] Top 20 Convergence of a regularization algorithm for nonexpansive and monotone operators in Hilbert spaces

... Many important problems have reformulations which require finding solutions of equi- libriums (.) and (.), for instance, image recovery, inverse problems, network alloca- tion, transportation problems and optimization ... See full document

... The rest of this paper is organized as follows. Section  contains some important facts and tools. In Section , we introduce a new iterative scheme for finding a common ele- ment of the fixed-point set of a ... See full document

... The rest of this paper is organized as follows. In order to prove our main results, some useful facts and tools are listed as lemmas in the next section. In Section , we prove that if a contractive mapping f in ... See full document

... proximal algorithm was proposed by Alvarez 7 in the context of convex ...maximal monotone operators. Recently, Moudafi 9 applied this algorithm for variational inequalities; Moudafi and ... See full document

... iteration algorithm for total quasi-ϕ-asymptotically nonex- pansive mapping to have the strong convergence under a limit condition in Banach ...quasi-ϕ-asymptotically nonexpansive multi-value mapping ... See full document

... strongly monotone mapping and B and G are two maximal monotone ...strong convergence theorem of the sequence generated by our iterative scheme is proved under suitable ...strong convergence ... See full document

... iterative algorithm (see ...strong convergence theorems of the sequence generated by the algorithm to a zero of the sum of two monotone operators and fixed point of mappings are ... See full document

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

... projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, ... See full document

... 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 ... See full document

... the regularization method for solving the variational inclusion problem of the sum of two monotone operators in Hilbert ...strong convergence theorem is then established under some ... See full document

... maximal monotone operators has emerged as an effective and powerful tool for studying many real world problems arising in various branches of social, physi- cal, engineering, pure and applied sciences in ... See full document

... weak convergence of PPA, many authors considered lots of different modifications; see [–] the references ...strong convergence theorems in Hilbert space without any compact assumption but with the ... See full document

... Remark 4.5. According to Corollaries 4.3 and 4.4, our assumptions are weaker than those of Song and Xu 11. Also, noticing that for a contraction f : X → X, the mapping 1/μI − f is strongly monotone and ... See full document

... arbitrary nonexpansive self-mappings on H with a common fixed point, S = { S ( t ) : 0 ≤ t < ∞} is a family of nonexpansive self- mappings on H such that T has property ( A ) with respect to the family S ... See full document

... In what follows, we always assume that H is a real Hilbert space with the inner product h·, ·i and the norm k · k. Let C be a nonempty, closed and convex subset of H. Let S : C → C be a mapping. F (S) denoted by ... See full document

... Lemma 2.5 Rockafellar 24. Let E be a smooth, strictly convex, and reflexive Banach space and let A ⊂ E × E ∗ be a monotone operator. Then A is maximal if and only if RJ rA E ∗ for all r > 0. Let E be a smooth, ... See full document

... In this paper, we study the existence and uniqueness of fixed points for a class of self-mappings satisfying certain rational expressions on closed, bounded and convex subsets with normal structures in reflexive Banach ... See full document

... Throughout this work, we always assume that H is a real Hilbert space, whose inner product and norm are denoted by ·, · and · , respectively. Let C be a nonempty closed convex subset of H and A a nonlinear ... See full document