Cho Yeol Je

Cho Yeol Je
Gyeongsang National University | GNU · Department of Mathematics Education

Professor and Ph. D.

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942
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15,119
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Publications

Publications (942)
Article
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In this paper, we introduce a stochastic self-adaptive subgradient extragradient approximation algorithm for solving the stochastic pseudomonotone variational inequality problem. The new method uses a variable stepsize generated by the simple computation at each iteration. Contrary to many known algorithms, the resulting algorithm can be easily imp...
Article
Full-text available
In this paper, a projection-type method is proposed for solving a variational inequality problem involving a monotone and Lipschitz continuous operator in a Hilbert space. One only projection in the method is used per each iteration. The strong convergence of iterative sequences generated by the method is established under suitable conditions impos...
Article
Full-text available
In this paper, we propose a new modified subgradient extragradient method for solving equilibrium problems involving pseudomonotone and Lipchitz-type bifunctions in Hilbert spaces. We establish the strong convergence of the proposed method under several suitable conditions. In addition, the linear convergence is obained under strong pseudomonotonic...
Article
Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more. In this work we are concern with the problem of finding a common solution of a monot...
Article
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In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm. Further, we give some applications for the convex minimization problem and the fixed point problem in CAT(κ) spaces with the...
Article
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In this paper, we introduce two simple inertial algorithms for solving the split variational inclusion problem in Banach spaces. Under mild and standard assumptions, we establish the weak and strong convergence of the proposed methods, respectively. As theoretical realization we study existence of solutions of the split common fixed point problem i...
Preprint
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It is well-known that the use of Bregman divergence is an elegant and effective technique for solving many problems in applied sciences. In this paper, we introduce and analyze two new inertial-like algorithms with Bregman divergence for solving pseudomonotone variational inequalities in a real Hilbert space. The first algorithm is inspired by Halp...
Article
For any fixed \(s \in \left\{ z \in \mathbb {C} : z \ne 0 \text { and } |z| <1 \right\} ,\) we consider the following functional inequality: $$\begin{aligned}&\nonumber \Vert f(a+a', c+c') + f(a+a', c-c') + f(a-a', c+c') + f(a-a', c-c')\nonumber \\&\quad -4f(a,c)-4f(a,c')\Vert \le \Bigg \Vert s \Bigg (2f\left( a+a', c-c'\right) + 2f\left( a-a', c+c...
Article
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The purpose of this paper is to introduce a new modified subgradient extragradient method for finding an element in the set of solutions of the variational inequality problem for a pseudomonotone and Lipschitz continuous mapping in real Hilbert spaces. It is well known that for the existing subgradient extragradient methods, the step size requires...
Article
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In this paper, we revisit the modified forward–backward splitting method (MFBSM) for solving a variational inclusion problem of the sum of two operators in Hilbert spaces. First, we introduce a relaxed version of the method (MFBSM) where it can be implemented more easily without the prior knowledge of the Lipschitz constant of component operators....
Article
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Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays wh...
Article
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The split feasibility problem is to find a point x * with the property that x * ∈ C and Ax * ∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y , respectively, and A is a bounded linear operator from X to Y. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensit...
Chapter
The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: yn=xn+αn(xn-xn-1),zn=xn+βn(xn-xn-1),xn+1=(1-λn)yn+λnT(zn)for each n≥1 and showed its convergence with the control conditions αn,βn∈[0,1). In this paper, we present the convergence analysis of the general inertial Krasnosel’skiǐ–Mann algorithm with the control conditions α...
Chapter
In this chapter, we introduce the new concept of the joint common limit in the range property (shortly, (JCLR)-property) in Sb-metric spaces and prove some common fixed point theorems by using the JCLR-property in Sb-metric spaces without the completeness of Sb-metric spaces. We also give some examples to illustrate our results. As applications of...
Article
In this paper, we revisit the subgradient extragradient method for solving a pseudomonotone variational inequality problem with the Lipschitz condition in real Hilbert spaces. A new algorithm based on the subgradient extragradient method with the technique of choosing a new step size is proposed. The weak convergence of the proposed algorithm is es...
Article
Full-text available
In this paper, we consider an improvement of the extragradient method to figure out the numerical solution for pseudomonotone equilibrium problems in arbitrary real Hilbert space. A new method is proposed with an inertial scheme and a self adaptive step size rule that is revised on each iteration based on the previous three iterations. The weak con...
Article
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In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The...
Article
Full-text available
In this work, we propose a new modified Popov’s method by using inertial effect for solving the variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration as well as it does not need to the...
Article
Full-text available
The purpose of this article is to propose an algorithm for finding an approximate solution of a split variational inclusion problem for monotone operators. By using inertial method, we get a new and simple algorithm for such a problem. Under standard assumptions, we study the strong convergence theorem of the proposed algorithm. As application, we...
Chapter
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In this paper, we consider convergence analysis of the solution sets for vector quasi-variational inequality problems of the Minty type. Based on the nonlin-ear scalarization function, we obtain a key assumption (H h) by virtue of a sequence of gap functions. Then we establish the necessary and sufficient conditions for the Painlevé-Kuratowski lowe...
Book
This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansi...
Article
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In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a...
Article
In this paper, we propose a single projection method for finding a solution of the bilevel pseudo-monotone variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm requires only one projection onto the feasible set. Also, we prove strong convergence theorems of the proposed method under mild conditions, which i...
Article
In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the framework of Hilbert spaces. First, we introduce a new iterative scheme which combines the inertial subgradient extragradient method with viscosity technique and with self-adaptive...
Chapter
In this paper, we introduce and study a new hybrid iterative method for finding a common solution of a mixed equilibrium problem and a fixed point problem for an infinitely countable family of closed quasi-Bregman strictly pseudocontractive mappings in reflexive Banach spaces. We prove that the sequences generated by the hybrid iterative algorithm...
Article
This paper introduces a new class of equilibrium problems named general regularized nonconvex mixed equilibrium problem. By using the auxiliary principle technique, some predictor–corrector methods for solving such class of general regularized nonconvex mixed equilibrium problems are suggested and analyzed. The study of convergence analysis of the...
Article
Full-text available
In this paper, we introduce a new algorithm which combines the inertial contraction projection method and the Mann-type method (Mann in Proc. Am. Math. Soc. 4:506–510, 1953) for solving monotone variational inequality problems in real Hilbert spaces. The strong convergence of our proposed algorithm is proved under some standard assumptions imposed...
Article
In this paper, we proposed a modified subgradient extragradient method for dealing with pseudomonotone equilibrium problems involving Lipschitz-type condition on a cost bifunction in a real Hilbert space. The weak convergence theorem for the method is precisely provided based on the standard assumptions on the cost bifunction. For a numerical exper...
Article
In this paper, we prove the weak convergence of a modified extragradient algorithm for solving a variational inequality problem involving a pseudomonotone operator in an infinite dimensional Hilbert space. Moreover, we establish further the R-linear rate of the convergence of the proposed algorithm with the assumption of error bound. Several numeri...
Article
Let X, Y be Hilbert spaces and F : X → Y be Frechet differentiable. Suppose that F′ is center-Lipschitz on U(w, r) and F′(w) be a surjection. Then, S1 = F(U(w, ε1)) is convex where ε1 ≤ r. The set S1 contains the corresponding set given in [18] under the Lipschitz condition. Numerical examples where the old conditions are not satisfied but the new...
Article
In this paper, we introduce a new class of generalized multiobjective games with fuzzy mappings and study the solution existence for this class of games. The model of bounded rationality proposed by Anderlini and Canning (2001) and Miyazaki and Azuma (2013) is applied to a new class of generalized multiobjective games with fuzzy mappings in infinit...
Article
Full-text available
In this paper, we introduce a new algorithm for solving variational inequality prob lems with monotone and Lipschitz-continuous mappings in real Hilbert spaces. Our algorithm requires only to compute one projection onto the feasible set per iteration. We prove under certain mild assumptions, a strong convergence theorem for the pro posed algorithm...
Article
Full-text available
In this work, we propose a new modified Popov’s method by using inertial effect for solving the variational inequality problem in real Hilbert spaces. The advantage of the proposed algorithm is the computation of only one value of the inequality mapping and one projection onto the admissible set per one iteration as well as it does not need to the...
Article
Full-text available
In this paper, we introduce a new algorithm which combines the inertial projection and contraction method and the viscosity method for solving monotone variational inequality problems in real Hilbert spaces and prove a strong convergence theorem of our proposed algorithm under the standard assumptions imposed on cost operators. Finally, we give som...
Article
Full-text available
In this paper, two algorithms are proposed for a class of pseudomonotone and strongly pseudomonotone equilibrium problems. These algorithms can be viewed as a extension of the paper title, the extragradient algorithm with inertial effects for solving the variational inequality proposed by Dong et al. (Optimization 65:2217–2226, 2016. https://doi.or...
Article
This paper proposes two algorithms that are based on a subgradient and an inertial scheme with the explicit iterative method for solving pseudomonotone equilibrium problems. The weak convergence of both algorithms is well-established under standard assumptions on the cost bifunction. The advantage of these algorithms is that they did not require an...
Article
The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical examp...
Article
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This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive map...
Article
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Let C be a closed affine subset of a real Hilbert space H and \(T:C \rightarrow C\) be a nonexpansive mapping. In this paper, for any fixed u ∈ C, a general Halpern iteration process: $$\left\{\begin{array}{ll} x_{0} \in C,\\ x_{n + 1}=t_{n}u+(1-t_{n})Tx_{n},n\geq 0, \end{array}\right. $$ is considered for finding a fixed point of T nearest to u, w...
Article
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In this paper, we introduce two golden ratio algorithms with new stepsize rules for solving pseudomonotone and Lipschitz variational inequalities in finite dimensional Hilbert spaces. The presented stepsize rules allow the resulting algorithms to work without the prior knowledge of the Lipschitz constant of operator. The first algorithm uses a sequ...
Article
In this paper, we introduce a viscosity extragradient method with Armijo linesearch rule to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive nonself-mapping in Hilbert space. The strong convergence of the algorithm is proved. As the application, a common fixed point theorem for two...
Article
Full-text available
In this paper, we introduce the notion of an orthogonal F-contraction mapping and establish some fixed point results for such contraction mappings in orthogonally metric spaces. Also, we give some examples which claim that the main results are generalizations of the Wardowski’s fixed point theorem. As applications of the main results, we apply our...
Article
Full-text available
Abstract This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function. The advantage of these algorithms was that they d...
Article
In this paper, we introduce a new algorithm for solving a variational inequality problem in a Hilbert space. The algorithm originates from an explicit discretization of a dynamical system in time. We establish the convergence of the algorithm for a class of non-monotone and Lipschitz continuous operators, provided by the sequentially weak-to-weak c...
Article
In this paper, we propose two inertial algorithms with new stepsize rule for solving a monotone and Lipschitz variational inequality in a Hilbert space and prove some weak and strong convergence theorems of the proposed inertial algorithms. The algorithms use variable stepsizes which are updated at each iteration by a simple computation without any...
Article
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In this paper, first, we introduce a new iterative algorithm involving demicontractive mappings in Hilbert spaces and, second, we prove some strong convergence theorems of the proposed method with the Armijo-line search to show the existence of a solution of the split common fixed point problem. Finally, we give some numerical examples to illustrat...
Article
Full-text available
In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based on the inertial subgradient extragradient algorithm, the viscosity approximation method and the Mann type method, and prove some strong convergence theorems for the proposed algorithms under suitable...
Article
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In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results...
Article
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Based on the very recent work by Shehu and Agbebaku in Comput. Appl. Math. 2017, we introduce an extension of their iterative algorithm by combining it with inertial extrapolation for solving split inclusion problems and fixed point problems. Under suitable conditions, we prove that the proposed algorithm converges strongly to common elements of th...
Article
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In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S−metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the theoretical results, we also present some illustrative examples to ve...
Article
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In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ–Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of th...
Article
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p>Fixed point theory in fuzzy metric spaces plays very important role in theory of nonlinear problems in applied science. In this paper, we prove an existence result of common fixed point of four nonlinear mappings satisfying a new type of contractive condition in a generalized fuzzy metric space, called weak non-Archimedean fuzzy metric space. Our...