• 대한수학회논문집
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• 제31권4호
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• pp.845-855
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• 2016

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

• 대한수학회지
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• 제53권5호
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• Restorative Dentistry and Endodontics
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• 제37권2호
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• pp.114-118
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• 2012

인접면의 우식증으로 인해 인접면의 공간 소실과 후방치아의 근심 경사가 발생한 본 증례에서 치아의 보철 수복 전 교정용 링의 삽입과 임시 전장관의 수정을 통해 치간 공간의 획득과 치축의 개선을 시행할 수 있었다.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.1-11
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• 2021

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.

• East Asian mathematical journal
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• 제27권5호
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• pp.545-555
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• 2011

Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• 대한수학회논문집
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• 제25권2호
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• pp.313-325
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• 2010

General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• 대한소아치과학회지
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• 제36권3호
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• pp.387-393
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• 2009

본 연구는 상악 유전치부의 치간공간과 인접면 우식의 상관관계를 평가해보고자 하였다. 익산에 거주하는 만3-7세의 어린이 555명을 대상으로 하였으며 탐침이 통과하는지 여부로 치간공간이 있음과 없음으로 분류하였고 와동이 형성되었거나 법랑질 표면이 연화되었을 경우 인접면 우식이 존재하는 것으로 판단하였다. 연구 결과 다음과 같은 결론을 얻었다. 1. 상악 유전치부의 치간공간은 영장류 공간이 77.4%, 발육공간이 유측절치와 유중절치 사이에서 54.4%, 양유중절치 사이에서 39.0%로 나타났다. 2. 인접면 우식발생율은 우측유견치가 6.3%, 우측유측절치가 14.7%, 우측유중절치가 33.5%, 좌측유중절치가 33.7%, 좌측유측절치가 16.0%, 좌측유견치가 4.7%로 나타났다. 3. 치간공간의 수가 많을수록 상악 유전치의 우식발생율은 낮아졌으나 그 상관관계(r=-0.024)는 미약하였다. 4. 상악 유전치부에 공간이 존재하지 않을 경우 존재할 때 보다 평균 우식발생율이 높았으며, 치간공간이 전혀 존재하지 않는 경우 한 곳이라도 치간공간이 존재하는 경우보다 평균 우식발생율이 2배 이상 높은 것으로 나타났다.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.749-780
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• 2021

In this paper, we give the notion of M(., .)-𝜂-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(., .)-𝜂-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.