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.     

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅱ)

By applying coincidence theorems in part (Ⅰ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in preceding paper, some new existence theorems for system of vector equilibrium problems, system of inequalities and system of minimax theorems were established in FC-spaces. These results generalize some known results in recent literature.     

Sharp Gagliardo–Nirenberg Inequalities and Mass Transport Theory

It is known that best constants and extremals of many geometric inequalities can be obtained via the Monge–Kantorovich theory of mass transport. But so far this approach has been successful for a special subclass of the Gagliardo–Nirenberg inequalities, namely, those for which the optimal functions involve only power laws. In this paper, we explore the link between Mass transport theory and all classes of the Gagliardo–Nirenberg inequalities. Sharp constants and optimal functions of all the Gagliardo–Nirenberg inequalities are obtained explicitly in dimension n = 1, and the link between these inequalities and Mass transport theory is discussed.     

Generalized gap functions and error bounds for generalized variational inequalities

We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.     

Existence and algorithm of solutions for general multivalued mixed implicit quasi-variational inequalities

A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the e     

On Hardy-type integral inequalities

The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte(C-P) type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.     

New Conservation Laws of Energy and C-D Inequalities in Continua with Microstructure

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New Conservation Laws of Energy and C-D Inequalities in Continua Without Microstructure

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｔｉｎｕｕｍｍｅｃｈａｎｉｃｓｉｓｎｏｔｏｎｌｙａｎｏｌｄａｎｄｂｕｔａｌｓｏａｙｏｕｎｇｓｃｉｅｎｔｉｆｉｃｄｉｓｃｉｐｌｉｎｅ.Ｉｔｃｏｎｓｉｓｔｓｏｆｓｏｍｅｆｕｎｄａｍｅｎｔａｌｌａｗｓ,ｗｈｉｃｈａｒｅｖａｌｉｄｆｏｒａｌｌｂｏｄｉｅｓｉｒｒｅｓｐｅｃｔｉｖｅｏｆｔｈｅｉｒｓｈａｐｅｓ,ｃｏｎｓｔｉｔｕｔｉｏｎｓａｎｄｃｏｎｓｔｉｔｕｔｉｖｅｒｅｌａｔｉｏｎｓ,ｗｈｉｃｈｍｕｓｔｒｅｆｌｅｃｔｔｈｅｎａｔｕｒｅｏｆｔｈｅｍａｔｅｒｉａｌａｎｄｔｈｅｃｏｎｓｔｉ…     

On the existence and uniqueness of solutions for a class of variational inequalities with applications to the signorini problem in mechanics

In this paper,we introduce a new unified and general class of variational inequalities,and show some existence and uniqueness results of solutions for this kind of variationalinequalities.As an application,we utilize the results presented in this paper to study theSignorini problem in mechanics.