• 대한수학회보
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• 제49권4호
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• pp.749-759
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• 2012

A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.

• 대한수학회보
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• 제56권3호
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• 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.

• Clinics in Shoulder and Elbow
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• 제6권2호
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• pp.149-160
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• 2003

Purpose: to determine the results after open intramedullary nailing and tension band suture technique in proximal humerus fracture for improving the stability and decreasing the complications. Materials and Method: Authors reviewed 27 patients treated by open intramedullary nailing and tension band suture technique. Mean follow-up period was 39 months (24-59months). Surgical neck fracture were 6 cases, surgical neck fracture with shaft fracture were 3 cases, three part fracture with greater tuberosity fracture were 17 cases, four part fracture was 1 case and fracture and dislocation were 2 cases Results: We got the bony union in 26 cases. Average pain scale was 1 point (0-6), Neer score was 86 point(45-99) and ASES score was 85 point(40-100). We separate all cases in two groups based on age (65 years), L-spine t-score (-2.5) and Neer classification (2 and 3 part). There is no significance in pain scale, Neer score and ASES score between each group. Conclusion: As a method of surgical treatment on severe proximal humeral fractures, we recommend intramedullary nailing and tension band suture technique and it may have particular advantages in early exercise and satisfactory functional outcome.

• Archives of Reconstructive Microsurgery
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• 제5권1호
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• pp.106-111
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• 1996

Purpose : Propose a surgical technique in donor harvesting method in free vascularized proximal fibular epiphysis. Methodology : Concerned about growth potentials of the transplanted epiphysis in our long term results of the epiphyseal transplanted 13 cases more than 4 years follow-up, anterior tibial artery which contains anterior tibial recurrent artery is most reliable vessel to proximal fibular epiphysis which is the best donor of the free vascularized epiphyseal transplantation. In vascular anatomical aspect proximal fibular epiphysis norished by latearl inferior genicular artery from popliteal, posterior tibial recurrent artery and anterior tibial recurrent artery from anterior tibial artery and peroneal artery through metaphysis. The lateral inferior genicular artery is very small and difficult to isolate, peroneal artery from metaphysis through epiphyseal plate can not give enough blood supply to epiphysis itself. The anterior tibial artery which include anterior tibial recurrent and posterior tibial recurrent artery is the best choice in this procedure. But anterior tibial recurrent artery merge from within one inch from bifucating point of the anterior and posterior tibial arteries from popliteal artery. So it is very difficult to get enough vascular pedicle length to anastomose in recipient vessel without vein graft even harvested from bifucating point from popliteal artery. Authors took recipient artery from distal direction of anterior tibial artery after ligation of the proximal popliteal side vessel, which can get unlimited pedicle length and safer dissection of the harvesting proximal fibular epiphysis. Results : This harvesting procedure can performed supine position, direct anterolateral approach to proximal tibiofibular joint. Dissect and isolate the biceps muscle insertion from fibular head, micro-dissection is needed to identify the anterior tibial recurrent arteries to proximal epiphysis, soft tissue release down to distal and deeper plane to find main anterior tibial artery which overlying on interosseous membrane. Special care is needed to protect peroneal nerve damage which across the surgical field. Conclusions : Proximal fibular epiphyseal transplantation with distally directed anterior tibial artery harvesting technique is effective and easier dissect and versatile application with much longer arterial pedicle.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1249-1262
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• 2010

An approximate alternating linearization decomposition method, for minimizing the sum of two convex functions with some separable structures, is presented in this paper. It can be viewed as an extension of the method with exact solutions proposed by Kiwiel, Rosa and Ruszczynski(1999). In this paper we use inexact optimal solutions instead of the exact ones that are not easily computed to construct the linear models and get the inexact solutions of both subproblems, and also we prove that the inexact optimal solution tends to proximal point, i.e., the inexact optimal solution tends to optimal solution.

• 대한수학회논문집
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• 제34권2호
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• pp.671-684
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• 2019

In this paper, we propose a new interior point method for solving nonlinear complementarity problems. In this method, we use a new profitable searching direction and instead of using the logarithmic quadratic term, we use a square root quadratic term. We prove the global convergence of the proposed method under the assumption that F is monotone. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Clinics in Shoulder and Elbow
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• 제19권4호
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• pp.216-222
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• 2016

Background: We investigated the effectiveness of fibular strut allograft augmentation of proximal humerus fractures to prevent varus deformity in patients over the age of 65 years with insufficient medial support. Methods: We analyzed the clinical and radiological outcomes of locking plate fixation with adjunct fibular strut allograft augmentation in 21 patients with proximal humeral fractures. The inclusion criteria were age (65-year-old or older); presence of severe medial comminution; inadequate medial support; and those who could participate in at least a one year follow-up. The average age was 76.4 years. We analyzed each patient's Constant score, our indicator of clinical outcome. As radiological parameters, we analyzed time-to-bone union; restoration of the medial hinge; difference between the immediately postoperative and the last follow-up humeral neck-shaft angles;; and anatomical reduction status, which was assessed using the Paavolainen method. Results: A successful bone union was achieved in all patients at an average of 11.4 weeks. We found that the average Constant score was 74.2, showing a satisfactory outcome. The average difference in the humeral neck-shaft angles between the immediately postoperative time-point and at the final follow-up was $3.09^{\circ}$. According to the Paavolainen method, the anatomical reduction was rated excellent. The medial hinge was restored in 14 of 21 patients. Although we did not find evidence for osteonecrosis, we found that a single patient had a postoperative complication of screw cut-out. Conclusions: Fibular strut allografting as an adjunct treatment of proximal humeral fractures may reduce varus deformity in patients with severe medial comminution.

• Journal of Korean Neurosurgical Society
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• 제53권3호
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• pp.150-154
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• 2013

Objective : To evaluate the effect of electromagnetic (EM) navigation system on ventriculoperitoneal (VP) shunt failure rate through comparing the result of standard shunt placement. Methods : All patients undergoing VP shunt from October 2007 to September 2010 were included in this retrospective study. The first group received shunt surgery using EM navigation. The second group had catheters inserted using manual method with anatomical landmark. The relationship between proximal catheter position and shunt revision rate was evaluated using postoperative computed tomography by a 3-point scale. 1) Grade I; optimal position free-floating in cerebrospinal fluid, 2) Grade II; touching choroid or ventricular wall, 3) Grade III; tip within parenchyma. Results : A total of 72 patients were participated, 27 with EM navigated shunts and 45 with standard shunts. Grade I was found in 25 patients from group 1 and 32 patients from group 2. Only 2 patients without use of navigation belonged to grade III. Proximal obstruction took place 7% in grade I, 15% in grade II and 100% in grade III. Shunt revision occurred in 11% of group 1 and 31% of group 2. Compared in terms of proximal catheter position, there was growing trend of revision rate according to increase of grade on each group. Although infection rate was similar between both groups, the result had no statistical meaning (p=0.905, chi-square test). Conclusion : The use of EM navigation in routine shunt surgery can eliminate poor shunt placement resulting in a dramatic reduction in failure rates.