Chih-Sheng Chuang

Mathematical programming with multiple sets split monotone variational inclusion constraints

In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two numerical examples are given to demonstrate our results.As applications of our convergence theorem of the hierarchical problem, we study the unique solution for the following problems: mathematical programming with multiply sets split variational inclusion and fixed point set constraints; mathematical programming with multiple sets split variational inequalities and fixed point set constraints; the variational inequality problem with a system of mixed type equilibria and fixed point set constraints; the variational inequality problem with multiple sets split system of mixed type equilibria and fixed point set constraints; mathematical programming with a system of mixed type equilibria and fixed point set constraints. We give iteration processes for these types of problems and establish the strong convergence for the unique solution of these problems. For our special case, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibria problem; the minimum norm solution of the system of mixed type equilibria problem. Our results will have many applications in diverse fields of science.

Solutions for a variational inclusion problem with applications to multiple sets split feasibility problems

In this paper, we first study the set of common solutions for two variational inclusion problems in a real Hilbert space and establish a strong convergence theorem of this problem. As applications, we study unique minimum norm solutions of the following problems: multiple sets split feasibility problems, system of convex constrained linear inverse problems, convex constrained linear inverse problems, split feasibility problems, convex feasibility problems. We establish iteration processes of these problems and show the strong convergence theorems of these iteration processes.MSC:47J20, 47J25, 47H05, 47H09.

Fixed point theorems for some new nonlinear mappings in Hilbert spaces

In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, like nonexpansive mappings and nonspreading mappings. We prove fixed point theorems, ergodic theorems, demiclosed principles, and Rays type theorem for these nonlinear mappings.Next, we prove weak convergence theorems for Moudafis iteration process for these nonlinear mappings. Finally, we give some important examples for these new nonlinear mappings.

Fixed point theorems and Δ-convergence theorems for generalized hybrid mappings on CAT(0) spaces

In this paper, we introduce generalized hybrid mapping on CAT(0) spaces. The class of generalized hybrid mappings contains the class of nonexpansive mappings, nonspreading mappings, and hybrid mappings. We study the fixed point theorems of generalized hybrid mappings on CAT(0) spaces. We also consider some iteration processes for generalized hybrid mappings on CAT(0) spaces, and our results generalize some results of fixed point theorems on CAT(0) spaces and Hilbert spaces.

Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces

In this paper, we prove both weak and strong convergence theorems for finding a common element of the solution set for a generalized equilibrium problem, the fixed point set of an asymptotically k-strict pseudo-contraction mapping in the intermediate sense, and the solution set of the variational inequality for a monotone and Lipschitz-continuous mapping by using a new hybrid extragradient method. Our results generalize and improve related results in the literatures.

Fixed point theorems for mappings with condition (B)

In this article, a new type of mappings that satisfies condition (B) is introduced. We study Pazys type fixed point theorems, demiclosed principles, and ergodic theorem for mappings with condition (B). Next, we consider the weak convergence theorems for equilibrium problems and the fixed points of mappings with condition (B).

Weak and strong convergence theorems of implicit iteration process on Banach spaces

In this article, we first consider weak convergence theorems of implicit iterative processes for two nonexpansive mappings and a mapping which satisfies condition (C). Next, we consider strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence theorem are different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent of a maximal monotone operator in a Banach space.

Convergence theorems of common fixed points for some semigroups of nonexpansive mappings in complete CAT(0) spaces

In this paper, we consider some iteration processes for one-parameter continuous semigroups of nonexpansive mappings in a nonempty compact convex subset C of a complete CAT(0) space X and prove that the proposed sequence converges to a common fixed point for these semigroups of nonexpansive mappings. Note that our results generalize Cho et al. result (Nonlinear Anal. 74:6050-6059, 2011) and related results.