caa a22 4500 463205952 CHVBK 20180405153126.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11228-006-0027-3 doi (NATIONALLICENCE)springer-10.1007/s11228-006-0027-3 Maingé Paul-Emile Département Scientifique Interfacultaire, GRIMMAG, Université des Antilles-Guyane, Campus de Schoelcher, 97230 Cedex, Martinique (F.W.I.), France aut Inertial Iterative Process for Fixed Points of Certain Quasi-nonexpansive Mappings [Elektronische Daten] [Paul-Emile Maingé] This paper deals with a general formalism which consists in approximating a point in a nonempty set $S$ , in a real Hilbert space $H$ , by a sequence $(x_n) \subset H$ such that $x_{{n + 1}} : = {\user1{\mathcal{T}}}_{n} {\left( {x_{n} + \theta _{n} {\left( {x_{n} - x_{{n - 1}} } \right)}} \right)}$ , where ${\left( {\theta _{n} } \right)} \subset \left[ {0,} \right.\left. 1 \right)$ , $x_0$ $x_1$ are in $H$ and ${\left( {{\user1{\mathcal{T}}}_{n} } \right)}_{{n \geqslant 0}}$ is a sequence included in a certain class of self-mappings on $H$ , such that every fixed point set of ${\user1{\mathcal{T}}}_{n}$ contains $S$ . This iteration method is inspired by an implicit discretization of the second order ‘heavy ball with friction' dynamical system. Under suitable conditions on the parameters and the operators ${\left( {{\user1{\mathcal{T}}}_{n} } \right)}$ , we prove that this scheme generates a sequence which converges weakly to an element of $S$ . In particular, by appropriate choices of ${\left( {{\user1{\mathcal{T}}}_{n} } \right)}$ , this algorithm works for approximating common fixed points of infinite countable families of a wide class of operators which includes $\alpha$ -averaged quasi-nonexpansive mappings for $\alpha \in {\left( {0,\;1} \right)}$ . Springer Science + Business Media B.V., 2006 Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 67-79 0927-6947 15:1<67 2007 15 11228 https://doi.org/10.1007/s11228-006-0027-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11228-006-0027-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Maingé Paul-Emile Département Scientifique Interfacultaire, GRIMMAG, Université des Antilles-Guyane, Campus de Schoelcher, 97230 Cedex, Martinique (F.W.I.), France aut NATIONALLICENCE 773 0- Set-Valued Analysis Kluwer Academic Publishers 15/1(2007-03-01), 67-79 0927-6947 15:1<67 2007 15 11228 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer