GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 996,Ｋｈａｍｓｉ[1]ｅｓｔａｂｌｉｓｈｅｄｔｈｅｈｙｐｅｒｃｏｎｖｅｘｖｅｒｓｉｏｎｏｆｔｈｅｆａｍｏｕｓＦａｎ＿ＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅ .Ｙｕａｎ[2 ,3]ｏｂｔａｉｎｓｏｍｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅｓ,ａｎｄａｓａｐｐｌｉｃａｔｉｏｎｓｏｆｔｈｅｉｒｒｅｓｕｌｔｓ,ｓｏｍｅｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓａｎｄｍａｔｃｈｉｎｇｔｈｅｏｒｅｍｓｆｏｒｏｐｅｎａ…     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

A parametric type of KKM theorem in <Emphasis Type="Italic">FC</Emphasis>-spaces with applications

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Combining magnetic resonance measurements with numerical simulations – Extracting blood flow physiology information relevant to the investigation of intracranial aneurysms in the circle of Willis

Cerebral aneurysms in the region of the circle of Willis have an incidence of 3–6% in western populations and involve the risk of rupture with subsequent subarachnoidal bleeding. The patient specific blood flow patterns are of substantial importance for understanding the pathogenesis of the lesions and may eventually contribute to deciding on the most efficient treatment procedure for a specific patient.A non-invasive method for performing in vivo measurements on blood velocity is 4D phase-contrast magnetic resonance angiography (PC-MRA), on the basis of which a flow field with all its parameters can be simulated. We are using this approach to investigate the hemodynamic parameters in the circle of Willis and, by analyzing the values at common locations of aneurysms, trying to find potential parameters to predict the development of aneurysms. Methodologically, we are acquiring the artery geometry with 3D-time-of-flight magnetic resonance (TOF) measurements and the blood velocity in the feeding arteries with 4D PC-MRA measurements in a healthy volunteer. These measurements are combined with computational fluid dynamics (CFD) to describe detailed hemodynamic patterns within the circle of Willis.     

On the existence of common fixed points for a pair of lipschitzian mappings in banach spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＫｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆａＢａｎａｃｈｓｐａｃｅＸ .ＴｈｅｎａｍａｐｐｉｎｇＴ :Ｋ→ＫｉｓｓａｉｄｔｏｂｅａＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇｉｆ,ｆｏｒｅａｃｈｉｎｔｅｇｅｒｎ≥ 1 ,ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｓｔａｎｔｋｎ >0ｓｕｃｈｔｈａｔ‖Ｔｎｘ-Ｔｎｙ‖ ≤ｋｎ‖ｘ-ｙ‖　ｆｏｒａｌｌｘ ,ｙ∈Ｋ .ＡＬｉｐｓｃｈｉｔｚｉａｎｍａｐｐｉｎｇＴｉｓｓａｉｄｔｏｂｅｕｎｉｆｏｒｍｌｙｋ＿Ｌｉｐｓｃｈｉｔｚｉａｎｉｆｋｎ =ｋｆｏｒａｌｌｎ ≥ 1 ;ｎｏ…     

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally <Emphasis Type="Italic">FC</Emphasis>-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.