• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.83-99
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• 2019

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.475-496
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• 2021

The main aim is to define a new class of generalized h-variational inequality problems and its generalized h-variational inequality problems. We define the class of h-𝜂-invex set, h-𝜂-invex function and H-pseudospace. Existence of the solution of the problems are established in H-pseudospace with the help of H-KKM mapping theorem and HC_*-condition of 𝜂 associated with the function h.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.421-436
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• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.307-332
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• 2024

Two inertial extragradient-type algorithms are introduced for solving convex pseudomonotone variational inequalities with fixed point problems, where the associated mapping for the fixed point is a 𝜌-demicontractive mapping. The algorithm employs variable step sizes that are updated at each iteration, based on certain previous iterates. One notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without necessitating any line search procedures. The iterative sequence constructed demonstrates strong convergence to the common solution of the variational inequality and fixed point problem under standard assumptions. In-depth numerical applications are conducted to illustrate theoretical findings and to compare the proposed algorithms with existing approaches.

• Journal of the Korean Institute of Landscape Architecture
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• v.31 no.4
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• pp.25-38
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• 2003

The main problems of disordered and congested urban landscape are due to the lack of holistic management that can control various elements of forming a city. Especially, the color of urban landscape is problematic because it is related to individual and social characteristics as well as to physical characteristics. Therefore, temporary expedients that can solve only visualized problems can not be a proper solution for color problems of urban landscape. This study originated from the question about why the color of disordered and congested urban landscape has not been improved. This study aims at directly improving the urban environmental color by finding out what the actual problems related to color are, and what the solutions would be. The goal of this study is to find a holistic systematic problem-solving method. Problems of urban environmental color are identified from both literature review and questionnaires to the expert group, such as environmental planning, design group, and the landscape executive group. Through mapping of relationships among these problems, the intellectual map was made to layout the structures of problems. Based on this method, the structures of problems of urban environmental color were classified into 5 categories: 1) the items related to the administrative structure, 2) the items related to the color management goal and system, 3) the items related to the color planning and design phase, 4) the items related to the color consulting committee, and 5) the items related to the present state of color use. Thus, in order to solve the color problem in urban landscape, practical strategy is strongly required. It is not a temporary expedient but a holistic approach. The solution for the problems of urban environmental color could be divided into 6 types; ‘regulations amendment’,‘color standard amendment’,‘color management plan’,‘color education’, and ‘advertisement for the goal of color management’. Regulations amendment among these types was proposed as the most effective method due to the close relationship with problem categories. Thus, as the solution for the problems of urban environmental color, the ‘color management system’ was suggested. Detailed contents the suggested color management system were divided into three parts; 1) legislation by regulations, ordinance and acts, 2) management by controling the level of guidelines, and 3) the standards for execution of this system.

• Journal of Environmental Science International
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• v.29 no.10
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• pp.951-959
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• 2020

This study aimed to re-establish the conservation area reflecting landscape ecological value through scenario program, targeting Odaesan National Park. The basic data were mapped in watershed planning units, which were set considering topographical and ecological values. The framework of Marxan with Zones, using an indexation process, was using the mapped indicators. Each best solution according to the scenarios was assessed through sensitivity analysis, and a final solution was selected among the best solutions, considering criteria including area ratio of conservation area and grouping. Lastly, the final solution was verified in the overlap analysis with recent zonation. As a result, through the framework of Marxan with Zones, the best solution of scenario 1, which was set by the highest conservation criteria was selected as the final solution, and the area ratio of conservation area and grouping was excellent. As for the overlap analysis, the suggested conservation area was improved compared to recent zonation in terms of the area ratio (39.4%), biotope grade I (35.6%) and the distribution points (7 places) of legally protected species.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.