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In this paper, for one thing, we introduce positively expansive system and positively expansive measure for nonautonomous dynamical systems. And we study the relation between positively expansive measure and the maximal cardinalities of separated set. We obtain the following main results. Firstly, we prove that every nonautonomous dynamical system with positively expansive measure implies there are e > 0 and a sequence of (n, e)-separated sets whose cardinalities go to infinite as n → ∞ . Secondly, we point out that every positively expansive system also implies the above properties. Thirdly, for each nonautonomous dynamical system that satisfies the above properties, there is a Borel probability measure such that the measure of the set of stable points of nonautonomous dynamical systems is zero. For another, we introduce positively countably expansive and positively measure expansive for nonautonomous dynamical systems. In addition, we prove that a nonautonomous dynamical system is positively measure expansive if and only if it is positively countably expansive. Finally, we introduce stable points and equicontinuous for a nonautonomous dynamical system and study some relevant properties. This paper primarily generalizes the main results obtained by Morales to nonautonomous dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm to find the common element of set of solutions of a split equilibrium problem and set of fixed points of an asymptotically nonexpansive mapping in Hilbert spaces. The new method is used to prove the strong convergence for the result of this paper. The result extends the corresponding one in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the split common fixed point problem for quasi-pseudo-contractive mappings is studied in Hilbert spaces. By using the hybrid projection method, a new algorithm and some strong convergence theorems are established under suitable assumptions. Our results not only improve and generalize some recent results but also give an affirmative answer to an open question. [ABSTRACT FROM AUTHOR]

In this paper, we consider a differential inclusion governed by a set-valued nonexpansive mapping and study the asymptotic behavior (weak and strong convergence) of its solutions with various assumptions on this mapping. Then for a set-valued nonexpansive mapping, we define the corresponding resolvent (proximal) operator as a set-valued mapping and study some of its elementary properties. Subsequently, we apply the resolvent operator to state the implicit discretization of the differential inclusion and study the asymptotic behavior of its solutions which yields similar convergence results as in the continuous case. This provides an algorithm for approximating a fixed point of a set-valued nonexpansive mapping which extends the classical proximal point algorithm. An application to variational inequalities and a numerical comparison with another iterative method for approximating a fixed point of set-valued nonexpansive mappings are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we prove weak and strong convergence theorems of SP-iteration for common fixed point of three G-nonexpansive mappings in uniformly convex Banach spaces endowed with a directed graph under some suitable control conditions. We also give some numerical examples for confirming our main theorem and compare convergence rate between SP-iteration and Noor iteration. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence theorem of the viscosity technique for the implicit midpoint rule of a nonexpansive mapping T in CAT(0) spaces. Under certain appropriate conditions on {αn}, we prove {xn} converges strongly to a fixed point of T which solves some variational inequality. Moreover, we give an application to the minimization problem. [ABSTRACT FROM AUTHOR]

In this paper, a new iterative scheme by hybrid projection method is proposed for a finite family of Bregman totally quasi-D-asymptotically nonexpansive mappings. Conditions ensuring strong convergence are imposed to common elements of set of common fixed points of the mappings and set of common solutions to a system of generalized mixed equilibrium problems in a reflexive Banach space. These results extend many important recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of xed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative method for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose new projection methods for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the solution set of a pseudomonotone equilibrium problem. The iterative schemes are based on the extended extragradient methods, fixed point methods, and Armijo-type linesearch techniques. We show that all of the iterative sequences generated by the scheme converge to the common element under mild assumptions on parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in Hilbert spaces, is introduced. For this method, a strong convergence theorem is given. This improves and extends some recent results. [ABSTRACT FROM AUTHOR]

In this paper, to find a common element of the fixed point set of common fixed points of a countable family of nonexpansive mappings and the solution set of the variational inequality for α-inverse-strongly monotone, we introduce an iterative approximation method in a real Hilbert space. Then the strong convergence theorem is proved under some appropriate conditions imposed on the parameters. This result extended and improved the corresponding results of Yao and Yao [15] and many others. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi [7]. [ABSTRACT FROM AUTHOR]

Using the concept of Bregman W-mapping, we propose a parallel hybrid extragradient algorithm for approximating a common element of the set of solutions of pseudomonotone equilibrium problems and split common fixed point problems of Bregman weak relatively nonexpansive mappings. With the algorithm, we state and prove a strong convergence result for finding a common solution of finite family of equilibrium problem and split common fixed point problem in a real Banach space. The stepsize for the split common fixed point problem is chosen in such a way that the algorithm does not require a prior estimation of the operator norm. Finally, we present an application of our results to variational inequality problems. Our result improves and extends some existing results in the literature in these directions. [ABSTRACT FROM AUTHOR]

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous generalized asymptotically nonexpansive mappings in Hilbert spaces. As a consequence, results on convergence to a common fixed point of a finite family of uniformly continuous asymptotically nonexpansive in the intermediate sense and asymptotically nonexpansive mappings are proved. [ABSTRACT FROM AUTHOR]