/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Fixed Point Theory

nonlinear functional analysis and its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear functional analysis and its applications is universally compatible with any devices to read.

Nonlinear Functional Analysis And Its Applications

Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces

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Theory Of Vector Optimization

A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.

Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F(S) of a nonexpansive mapping S and the set of solutions ? A of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approximation) method. The method produces three sequences which are shown to converge strongly to the same common element of $${F(S)\cap\Omega_{A}}$$ . As applications, the method provides an algorithm for finding the common fixed point of a nonexpansive mapping and a pseudocontractive mapping, or a common zero of a monotone Lipschitz continuous mapping and a maximal monotone mapping.

/pdf/strong-convergence-theorem-by-a-hybrid-extragradient-like-29brpx207m.pdf

Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set @C of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191-201], we propose an iterative algorithm for finding an element of Fix(S)@[email protected] We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)@[email protected] under mild conditions.

https://link.springer.com/content/pdf/10.1186%2Fs13663-015-0441-z.pdf

Lu-Chuan Ceng

Papers

A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

An extragradient method for solving split feasibility and fixed point problems