We prove the existence of strong solutions to a nonlinear evolution equation of the form  u′(t) + g(t) = f(t) + h(t) g ∈ SL2{∂φ(u(·))} f ∈ SL2{F (·, u(·))} u(0) = −u(T ), in a Hilbert space H, where φ : D(∂φ) ⊂ H → IR+ is a proper, convex, l.s.c. function of compact type, F : [ 0, T ]×D(∂φ)→ 2 is a multifunction which is demiclosed and dominated in some sense by ∂φ and h ∈ L(0, T ;H) is suf...

*Correspondence: [email protected] School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China Abstract In this paper, we prove the demiclosed principle for total asymptotically nonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergence theorems of the mixed Agarwal-O’Regan-Sahu type iteration for total asymptotically nonexpansive non...

* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, l...

Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...

* Correspondence: zhjx_19@yahoo. com.cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China Full list of author information is available at the end of the article Abstract Uniformly convex W-hyperbolic spaces with monotone modulus of uniform convexity are a natural generalization of both uniformly convexnormed spaces and CAT(0) spaces. In this article, we discuss ...

The weak convergence of the iterative generated by J(un+1 − un) = τ(Fun − Jun), n ≥ 0, ( 0 < τ = min { 1, 1 λ }) to a coincidence point of the mappings F, J : V → V ? is investigated, where V is a real reflexive Banach space and V ? its dual (assuming that V ? is strictly convex). The basic assumptions are that J is the duality mapping, J − F is demiclosed at 0, coercive, potential and bounded ...

&lt;p style='text-indent:20px;'&gt;In this paper, for solving the variational inequality problem over set of common fixed points a finite family demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between steepest-descent method and block-iterative ones. The strong convergence is proved without boundedly ...