• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.465-480
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• 2019

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K^{\varphi}_wf)_{w>0}$. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in $C({\mathbb{R}})$, the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$ for the family $(K^{\varphi}_wf)_{w>0}$. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.

• Journal of the Korea Society of Computer and Information
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• v.24 no.2
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• pp.41-48
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• 2019

Digital image watermarking techniques have been studied in various fields in order to protect the copyright of multimedia contents mostly composed by images. JPEG compression is a representative copyright attack for image watermarking. The CRT-based watermarking methods in DCT domain have been studied, because these are robust for JPEG compression attack. In this paper, we propose a new method with improved performance compared with the existing CRT based methods in DCT domain. The proposed method selects the DCT block according to the denseness at the watermark insertion phase, and iteratively adjust the CRT Conditional coefficients at the watermark extraction. This paper shows that it is more robust for the JPEG compression attacks through experimental results.

• Journal of information and communication convergence engineering
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• v.17 no.3
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• pp.167-173
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• 2019

This study investigates the problem of leader-following consensus for multi-agent systems with output saturations. This study assumes that the agents are described as a neutrally stable system, and the leader agent generates the bounded trajectory within the saturation level. Then, the objective of the leader-following consensus is to track the trajectory of the leader by exchanging information with neighbors. To solve this problem, we propose an observer-based distributed consensus algorithm. Then, we provide a consensus analysis by applying the Lyapunov stability theorem and LaSalle's invariance principle. The result shows that the agents achieve the leader-following consensus in a global sense. Moreover, we can achieve the consensus by choosing any positive control gain. Finally, we perform a numerical simulation to demonstrate the validity of the proposed algorithm.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.297-327
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• 2019

In this paper, we introduce and study a general iterative algorithm to approximate a common solution of split generalized equilibrium problem, variational inequality problem and fixed point problem for a finite family of nonexpansive mappings in real Hilbert spaces. Further, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Finally, we derive some consequences from our main result. The results presented in this paper extended and unify many of the previously known results in this area.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.523-558
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• 2021

In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature.

• Current Optics and Photonics
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• v.6 no.1
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• pp.1-9
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• 2022

This paper proposes a robust, simple zonal wavefront-estimation method in a grid sampling model. More slopes are added to the integral equation of the algorithm to improve the accuracy and convergence rate of this approach, especially for higher-order optical aberrations. The Taylor theorem is applied to clarify the mathematical description of the remaining error in the proposed method. Several numerical simulations are conducted to ensure the performance and improvement in comparison to the Southwell and previous algorithm. An experiment is also conducted according to deflectometry output and the results are verified using a reference measured with a stylus system.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.244-262
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• 2022

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H²-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.595-619
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• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.289-308
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• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.