Modified semi-implicit midpoint rule for nonexpansive mappings
نویسندگان
چکیده
منابع مشابه
Modified semi-implicit midpoint rule for nonexpansive mappings
where h > is a stepsize. It is known that if f :RN →RN is Lipschitz continuous and sufficiently smooth, then the sequence {xn} generated by (.) converges to the exact solution of (.) as h→ uniformly over t ∈ [, t̄] for any fixed t̄ > . If we write the function f in the form f (t) = g(t) – t, then differential equation (.) becomes x′ = g(t)– t. Then the equilibrium problem associated w...
متن کاملThe Implicit Midpoint Rule for Nonexpansive Mappings in Banach Spaces
The implicit midpoint rule (IMR) for nonexpansive mappings is established in Banach spaces. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a uniformly convex Banach space which either satisfies Opial’s property or has a Fréchet differentiable norm. Consequently, this algorithm applies in both `p and Lp for 1 < p < ∞.
متن کاملThe viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces
The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in...
متن کاملModified Iterative Algorithms for Nonexpansive Mappings
Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F S ∩ F T / ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn 1 βnxn 1 − βn Syn, yn αnγ...
متن کاملStrong Convergence of Modified Implicit Iteration Processes for Common Fixed Points of Nonexpansive Mappings
Throughout this paper, let H be a real Hilbert space with inner product 〈·,·〉 and norm ‖ · ‖. Let C be a nonempty closed convex subset of H , we denote by PC(·) the metric projection from H onto C. It is known that z = PC(x) is equivalent to 〈z− y,x− z〉 ≥ 0 for every y ∈ C. Recall that T : C → C is nonexpansive if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is a fixed point of T provided ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2015
ISSN: 1687-1812
DOI: 10.1186/s13663-015-0414-2