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Article
A unified Douglas–Rachford algorithm for generalized DC programming
We consider a class of generalized DC (difference-of-convex functions) programming, which refers to the problem of minimizing the sum of two convex (possibly nonsmooth) functions minus one smooth convex part. ...
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Article
Open AccessSplit proximal linearized algorithm and convergence theorems for the split DC program
In this paper, we study the split DC program by using the split proximal linearized algorithm. Further, linear convergence theorem for the proposed algorithm is established under suitable conditions. As applic...
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Article
Open AccessHybrid proximal linearized algorithm for the split DC program in infinite-dimensional real Hilbert spaces
To be the best of our knowledge, the convergence theorem for the DC program and split DC program are proposed in finite-dimensional real Hilbert spaces or Euclidean spaces. In this paper, to study the split DC...
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Article
Open AccessAn algorithm for the split-feasibility problems with application to the split-equality problem
In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality p...
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Article
Open AccessHybrid simultaneous algorithms for the split equality problem with applications
The split equality problem has board applications in many areas of applied mathematics. Many researchers studied this problem and proposed various algorithms to solve it. From the literature we know that most ...
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Article
Open AccessMathematical programming for the sum of two convex functions with applications to lasso problem, split feasibility problems, and image deblurring problem
In this paper, two iteration processes are used to find the solutions of the mathematical programming for the sum of two convex functions. In infinite Hilbert space, we establish two strong convergence theorem...
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Article
Open AccessNew strong convergence theorems for split variational inclusion problems in Hilbert spaces
The split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present a descent-conjugate gradient algorithm for the split vari...
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Article
Open AccessMathematical 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 convergen...
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Article
Open AccessStrong convergence theorems for the split variational inclusion problem in Hilbert spaces
In this paper, we first consider a split variational inclusion problem and give several strong convergence theorems in Hilbert spaces, like the Halpern-Mann type iteration method and the regularized iteration ...
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Article
Open AccessSolutions 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 un...
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Article
Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications
In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some map**. We also show...
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Article
New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces
Motivated by the Suzuki’s type fixed point theorems, we give several new existence theorems for scalar quasi-equilibrium problems, and vector quasi-equilibrium problem on complete metric spaces. We give import...
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Article
Halpern’s type iterations with perturbations in Hilbert spaces: equilibrium solutions and fixed points
In this paper, we consider an iteration process of Halpern’s type for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points for a quasi-nonexpansive map** wit...
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Article
Weak and strong convergence theorems for asymptotically pseudo-contraction map**s 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-c...
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Article
Open AccessConvergence theorems of common fixed points for some semigroups of nonexpansive map**s in complete CAT(0) spaces
In this paper, we consider some iteration processes for one-parameter continuous semigroups of nonexpansive map**s in a nonempty compact convex subset C of a complete CAT(0) space X and prove that the proposed ...
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Article
Open AccessWeak 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 map**s and a map** which satisfies condition (C). Next, we consider strong convergence theorem...
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Article
Open AccessFixed point theorems for map**s with condition (B)
In this article, a new type of map**s that satisfies condition (B) is introduced. We study Pazy's type fixed point theorems, demiclosed principles, and ergodic theorem for map**s with condition (B). Next, ...
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Article
Open AccessFixed point theorems for some new nonlinear map**s in Hilbert spaces
In this paper, we introduced two new classes of nonlinear map**s in Hilbert spaces. These two classes of nonlinear map**s contain some important classes of nonlinear map**s, like nonexpansive map**s an...
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Article
Open AccessFixed point theorems and Δ-convergence theorems for generalized hybrid map**s on CAT(0) spaces
In this paper, we introduce generalized hybrid map** on CAT(0) spaces. The class of generalized hybrid map**s contains the class of nonexpansive map**s, nonspreading map**s, and hybrid map**s. We stu...
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Article
Open AccessSaddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces
We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilib...
