# Nuttapol PakkaranangPhetchabun Rajabhat University · Mathematics and Computing Science Program

Nuttapol Pakkaranang

Doctor of Philosophy

Lecturer, Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University,

## About

65

Publications

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256

Citations

## Publications

Publications (65)

Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conju...

We propose a new proximal-type method to solve equilibrium problems in a real Hilbert space. The new method is analogous to the famous two-step extragradient method that is used to solve variational inequalities in the Hilbert spaces. The proposed iterative scheme uses a new non-monotone step size rule based on local bifunction information instead...

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assu...

The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The proposed iterative algorithms use a new step size rule b...

In this paper, a new algorithm is proposed to solve pseudo-monotone variational inequalities with the Lipschitz condition in a real Hilbert space. This problem is an exceptionally general mathematical problem in the sense that it consists of a number of the applied mathematical problems as a special instance, such as optimization problems, equilibr...

In this paper, we present improved iterative methods for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. The method is built around two computing phases of a proximallike mapping with inertial terms. Many such simpler step size rules that do not involve line searc...

Split variational inclusion problems are core and useful technique that connects many important problems in nonlinear analysis. This paper proposes a resolvent-based superiorization method for solving split variational inclusion problems, and some strong convergence theorems are proved under some mild conditions. Superiorization iterative procedure...

The main goal of this research is to solve variational inequalities involving quasi-monotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line searc...

Addressing crime detection, cyber security and multi-modal gaze estimation in biometric information recognition is challenging. Thus, trained artificial intelligence (AI) algorithms such as Support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS) have been proposed to recognize distinct and discriminant features of biometric i...

In this article, we present a new modified proximal point algorithm in the framework of CAT(1) spaces which is utilized for solving common fixed point problem and minimization problems. Also, we prove convergence results of the obtained process under some mild conditions. Our results extend and improve several corresponding results of the existing...

In this paper, we study the strong convergence of new methods for solving classical variational inequalities problems involving semistrictly quasimonotone and Lipschitz-continuous operators in a real Hilbert space. Three proposed methods are based on Tseng's extragradient method and use a simple self-adaptive step size rule that is independent of t...

This paper investigates the impact of Darcy number and variable thermal conductivity on MHD free convective heat transfer in a microchannel. Approximate solution of the problem is obtained by using semi-analytical method. Most of the fluid physical properties associated with flow are displayed, analyzed, and discussed. From the results, it is found...

Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ-demicontractive mapping. These inertial-type iterative methods use self-adaptive step size...

In this article, we present a blind deconvolution method for image restoration involving an adaptive point spread function. The method is introduced by applying concurrent optimization via simulating an image deblurring game. We assign the optimal image deblurring as a Nash equilibrium image deblurring game between three players based on three crit...

The purpose of this paper is to present $\Delta$-convergence and strong convergence theorems for quasi-nonexpansive sequences in the setting of geodesic space with curvature bounded above by one. The results can be applied to the image recovery problem for a countable family of closed convex subset of such spaces and also applied to the optimizatio...

The primary objective of this study is to introduce two novel extragradient-type iterative schemes for solving variational inequality problems in a real Hilbert space. The proposed iterative schemes extend the well-known subgradient extragradient method and are used to solve variational inequalities involving the pseudomonotone operator in real Hil...

Let R n be an Euclidean space and g : R n → R n be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ C s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear...

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...

In this paper, we study the numerical solution of the variational inequalities involving quasimonotone operators in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges strongly to a solution. The main advantage of the propo...

In this paper, we examine the weak convergence of a method to solve classical variational inequality problems involving quasimonotone and Lipschitz continuous operators in a real Hilbert space. The proposed method is inspired by Tseng's extragradient method and uses a simple self-adaptive step size rule that is independent of the Lipschitz constant...

The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function,...

The main objective of this study is to introduce a new two-step proximal-type method to solve equilibrium problems in a real Hilbert space. This problem is a general mathematical model and includes a number of mathematical problems as a special case, such as optimization problems, variational inequalities, fixed point problems, saddle time problems...

In this paper, a matrix-free method for solving large-scale system of nonlinear equations is presented. The
method is derived via quasi-Newton approach, where the approximation to the Broyden's update is done
by constructing diagonal matrix using acceleration parameter. A fascinating feature of the method is that
it is a matrix-free, so is suitable...

In this article, we present an inertial subgradient extragradient-type method that uses a non-monotone step size rule to find a numerical solution to equilibrium problems in real Hilbert spaces. The presented iterative scheme is based on an extragradient subgradient method and an inertial-type scheme. In fact, the proposed iterative scheme is effec...

In this paper, we propose a modified extragradient method for solving a strongly pseudomonotone equilibrium problem in a real Hilbert space. A strong convergence theorem relative to our proposed method is proved and the proposed method has worked without having the information of a strongly pseudomonotone constant and the Lipschitz-type constants o...

In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator info...

In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we pro...

The objective of this paper is to introduce an iterative method with the addition of an inertial term to solve equilibrium problems in a real Hilbert space. The proposed iterative scheme is based on the Mann-type iterative scheme and the extragradient method. By imposing certain mild conditions on a bifunction, the corresponding theorem of strong c...

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space. 0

In this paper, we introduce a subgradient extragradient method to find the numerical solution of strongly pseudomonotone equilibrium problems with the Lipschitz-type condition on a bifunction in a real Hilbert space. The strong convergence theorem for the proposed method is precisely established on the basis of the standard cost bifunction assumpti...

In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bou...

In this paper, we are introducing a new algorithm that is based on a subgradient and an inertial scheme using an explicit method for step size evaluation to solve pseudomonotone equilibrium problems. The weak convergence theorem for an algorithm is well established on the basis of standard cost bifunction conditions. A useful feature of a method th...

Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities prob...

A number of applications from mathematical programmings, such as minimax problems, penalization methods and fixed-point problems can be formulated as a variational inequality model. Most of the techniques used to solve such problems involve iterative algorithms, and that is why, in this paper, we introduce a new extragradient-like method to solve t...

The primary objective of this study is to present a new self-adaptive method to solve an equilibrium problem involving pseudomonotone bifunction in real Hilbert spaces. This method could be viewed as an improvement of the paper title Extragradient algorithms extended to equilibrium problem by Tran et al. [D.Q. Tran, M.L. Dung, V.H. Nguyen, Extragra...

The aim of this paper is to introduce the notion of a multivalued Gerghaty type contractive mapping via simulation functions along with C-class functions and prove some fixed point results. As consequences, we derive some fixed point results endowed with graph. An example is given to show the validity of our results given herein. MSC: 54H25; 47H10

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...

A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introduced a new extragradient-like method to solve equil...

Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the pseudomonotone equilibrium in real Hilbert space. This method uses a non-monotonically stepsize techniqu...

In this paper, we suggest a new method to solve the pseudomono-tone equilibrium problem. This method can be seen as an extension and improvement of the Popov's extragradient method. We replace the fixed stepsize with a self-adapting stepsize formula that is revised on each iteration depends on previous iterations. A weak convergence theorem of the...

In this article, we propose a new modified extragradient-like method to solve pseudomonotone equilibrium problems in real Hilbert space with a Lipschitz-type condition on a bifunction. This method uses a variable stepsize formula that is updated at each iteration based on the previous iterations. The advantage of the method is that it operates with...

In this paper, we propose the modified splitting method for accretive operators in Banach space and prove some strong convergence theorems of the proposed method under suitable conditions. Our main results can be viewed as the improvement of the results of Takahashi et al.¹. In deed, we remove the conditions that limn→∞ (rn + rn+1) = 0 in our resul...

The purpose of this paper to build up the concept of a Meir-Keeler condensing and integral type condensing operators in partially ordered Banach spaces via the concept of a measure of noncompactness. We also provide a characterization of a Meir-Keeler condensing operators using the notion of L-functions in partially ordered Banach spaces. To attain...

The aim of this paper is to bring and study the convergence behaviour of modified Picard-S iteration involving two G-nonexpansive mappings in CAT(0) space with directed graph. We prove ∆ and strong convergence theorems for modified Picard-S iteration process in CAT(0) space with a directed graph. We also construct a numerical example to validate ou...

The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ-convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non-trivial examples are also provided to show performance and comp...

In this paper, we are interested in solving minimization problem and common fixed point problem of finite family consisting asymptotically nonexpansive mappings in Hadamard spaces. For finding common solutions of their problems, we introduce a new modified proximal point algorithm involving convex combination technique. Under suitable conditions ,-...

In this paper, we introduce a generalized viscosity explicit method (GVEM) for nonexpansive mappings in the setting of Banach spaces and, under some new techniques and mild assumptions on the control conditions, prove some strong convergence theorems for the proposed method, which converge to a fixed point of the given mapping and a solution of the...

In this paper, we introduce a proximal point algorithm involving hybrid iteration for nonexpansive mappings in non-positive curvature metric spaces, namely CAT(0) spaces and also prove that the sequence generated by proposed algorithms converges to a minimizer of a convex function and common fixed point of such mappings.

In this paper, we construct a new type iterative scheme is so call
Picard-S hybrid with errors to prove Δ-convergence and strong convergence theorems under suitable conditions for total asymptotically nonexpansive mappings
in CAT(0) spaces. Our results in the paper improve and extend many results
appeared in the literature. Furthermore, we also ill...

Spectral gradient methods and projection technique have motivated many numerical methods for solving monotone equations. In this work, we proposed a hybrid spectral gradient algorithm for system of nonlinear monotone equations with convex constraints. The method is a combination of a convex combination of two different positive spectral parameters...

In this paper, we aim to introduce new four steps of proximal point
algorithm for nonexpansive mappings in non-positive curvature metric spaces,
namely CAT(0) spaces and also prove that the sequence generated by the proposed
algorithm converges to a minimizer of a convex function and common fixed
point of such mappings.

In this paper, we introduce a new modified proximal point algorithm for nonexpansive mappings in non-positive curvature metric spaces and also we prove the sequence generated by bluethe proposed algorithms converges to a common solution between minimization problem and fixed point problem. Moreover, we give some numerical examples to illustrate our...

In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and also prove some convergence theorems of the proposed algorithm to a common fixed point of asymptotically quasi-nonexpansive mappings and a minimizer of a convex function. The main results in th...

In this paper, we propose a new modiﬁed proximal point algorithm involving ﬁxed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm ∆-converges to a common solution between certain convex optimization and ﬁxed point problems.

In this paper, we introduce new type iterative scheme called a ‘modified Picard-S hybrid’ iterative algorithm to establish Δ-convergence and strong convergence theorems under suitable conditions for total asymptotically nonexpansive mappings in CAT(0) spaces. Our results in the paper improve and extend many results appeared in the literature. Moreo...

In this paper, we introduce a modiﬁed two-step viscosity iteration process for total asymptotically nonexpansive mappings in CAT(0) spaces. We prove strong convergence of the proposed iteration process to a ﬁxed point of total asymptotically nonexpansive mappings in CAT(0) spaces, which also shows that the limit of the sequence generated by propose...

In this paper, we modified multi-step procedure to find approximation fixed point of pairwise generalized nonexpansive mappings in CAT(0) spaces. We also prove both strong and \(\varDelta \)-convergence theorems for such a mapping with under mild conditions.

In this paper, we will introduce new random AKiterative process with errors for random contraction operator T in separable Banach spaces. We also prove that under satisfying some suitable conditions this iterative process with errors converges strongly to a random fixed point of T. Our results improves and extends the corresponding recent results w...

In this paper, we introduce AK iteration for finding fixed point of Suzuki generalized nonexpansive mappings in CAT(0) spaces. Under mild conditions, we also prove strong and $\Delta$ convergence theorems for Suzuki’s generalized nonexpansive mappings in CAT(0) spaces.

In this paper, we introduce modified Halpern iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces. Under some conditions, the strong convergence theorem is obtained.

In this paper, we introduce a modified viscosity implicit iteration for asymptotically nonexpansive mappings in complete CAT(0) spaces. Under suitable conditions, we prove some strong convergence to a fixed point of an asymptotically nonexpansive mapping in a such space which is also the solution of variational inequality. Moreover, we illustrate s...

In this paper, we prove some strong and ∆-convergence theorems of the modified S-iteration for (α, β)-generalized hybrid mappings in CAT(0) spaces. Our results improve and extend the corresponding recent results announced in [1] and some papers.