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A strong convergence theorem based on a relaxed extragradient method for generalized equilibrium problems
Nonexpansive mapping inverse-strongly monotone mapping
2010/9/21
In this paper, we introduce a new relaxed extragradient viscosity approximation method for finding the common element of the set of solutions of a generalized equilibrium problems, the set of common f...
Strong convergence theorem for solving equilibrium problems by hybrid method of asymptotically k-strictly pseudo-contractive mappings in Hilbert spaces
asymptotically k-strictly pseudo-contractive equilibrium problems
2010/9/14
In this paper, we introduce the iterative schemes by using hybrid methods for finding a common element of the set of an equilibrium problem and the set of fixed points of asymptotically k-strictly pse...
A convergence theorem via a new fixed point theorem for generalized contractions
τ -function τ 0-metric Nadler’s fixed point theorem
2010/9/13
In this paper, we study the properties of τ 0-metrics introduced and studied by Du [1], and establish a new fixed point theorem and convergence theorem for τ 0-metrics.
On convergence theorem for nonself I-nonexpansive mapping in Banach spaces
Mann and Ishikawa iterations nonself nonexpansive maps
2010/9/16
Suppose that E be a uniformly convex Banach space, let K be a nonempty convex subset of E with P as a nonexpansive retraction. Let T : K → E be a given nonself mapping. The modified Ishikawa iterative...
A new convergence theorem for Newton's method in Banach space using assumptions on the first Frechet-derivative
Newton’s method Fr´ echet-differentiable
2010/9/15
In this study, we provide a new Kantorovich-type convergence theorem for Newton’s method in Banach space. Its condition is different from earlier ones, and therefore it has theoretical and practical v...
On the Relationship between the Baum-Katz-Spitzer Complete Convergence Theorem and the Law of the Iterated Logarithm
partial sums of i.i.d. Banach space-valued random variables Baum--Katz--Spitzer complete convergence theorem law of the iterated logarithm almost sure convergence
2007/12/11
For a sequence of i.i.d. Banach space-valued random variables $\{X_{n}; ~n \geq 1 \}$ and a sequence of positive constants $\{a_{n}; ~n \geq 1 \}$, the relationship between the Baum--Katz--Spitzer com...
A SUPPLEMENT TO THE BAUM-KATZ-SPITZER COMPLETE CONVERGENCE THEOREM
partial sums of i.i.d. Banach space valued random variables Baum--Katz--Spitzer complete convergence theorem almost sure convergence
2007/12/11
Let $ \{X,~X_{n};~n \geq 1 \}$ be a sequence of i.i.d. Banach space valued random variables and let $\{a_{n}; ~n \geq 1 \}$ be a sequence of positive constants such that \[ a_{n} \uparrow \infty ~~\mb...