Pareto equilibria for generalized constrained multiobjective games in FC-spaces without local convexity structure

In this paper, we further study a class of generalized constrained multiobjective games where the number of players may be finite or infinite, the strategy sets may be general FC-spaces without local convexity structure, and all payoff functions get their values in infinite-dimensional topological vector spaces. By using an existence theorem of maximal elements for a family of set-valued mappings in FC-spaces due to the author, an existence theorem of solutions for a system of generalized vector quasivariational inclusions is first proved in general FC-spaces. By applying the existence result of solutions of the system of generalized vector quasivariational inclusions, some existence theorems of (weak) Pareto equilibria for the generalized constrained multiobjective games are established in noncompact product FC-spaces. Some special cases of our results are also discussed. Our results are new and different from the corresponding known results in the literature.     

Weak-type Endpoint Estimates for Multilinear Singular Integral Operators

In this paper, the authors discuss a class of multilinear singular integrals and obtain that the operators are bounded from H^1(R^n) to weak L^1(R^n). Using this result, we can directly prove a main theorem in [5].     

A Criterion for Designs in ℤ4-codes on the Symmetrized Weight Enumerator

The Assmus–Mattson theorem is known as a method to find designs in linear codes over a finite field. It is an interesting problem to find an analog of the theorem for Z ₄-codes. In a previous paper, the author gave a candidate of the theorem. The purpose of this paper is to give an improvement of the theorem. It is known that the lifted Golay code over Z ₄ contains 5-designs on Lee compositions. The improved method can find some of those without computational difficulty and without the help of a computer.     

On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p ⁿ are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain result of Macbeath, that such surfaces admit a symmetry which we shall call in this paper the Macbeath-Singerman symmetry. A classical theorem by Harnack states that the set of fixed points of a symmetry of a Riemann surface X of genus g consists of k disjoint Jordan curves called ovals for some k ranging between 0 and g+1. In this paper we show that given an odd prime p, a Macbetah-Singerman symmetry of Belyi surface with PSL(2,p) as a group of automorphisms has at most     

A generalized mixed vector variational-like inequality problem

In this paper, we introduce relaxed η-α-P-monotone mapping, and by utilizing KKM technique and Nadler’s Lemma we establish some existence results for the generalized mixed vector variational-like inequality problem. Further, we give the concepts of η-complete semicontinuity and η-strong semicontinuity and prove the solvability for generalized mixed vector variational-like inequality problem without monotonicity assumption by applying the Brouwer’s fixed point theorem. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.     

F-空间中的一个基本定理及其在数值分析中的应用

本文针对F-空间中闭算子方程的一般逼近格式,研究其相容性、收敛性和稳定性之间的关系.所得的主要结果是：这种一般逼近格式在相容性条件下,其收敛性与稳定性是等价的.此定理可以看作是对Lax等价原理的推广,是求解第一类闭算子方程的一般逼近格式的基本定理.为得到这一主要结果,本文还给出了F-空间中的一条基本定理,众所周知的一致有界原理,闭图像定理和开映像定理是其简单推论.     

Nonlinear Doob—Meyer Decomposition with Jumps

Concepts of g-supersolution ,g-martingale,g-supermartingale are introduced,wihch are related to BSDE with Brownian motion and Poisson Point process.A strict comparison theorem,monotonic limit theorem related to this type of BSDE are also discussed.As an application of these results,a nonlinear Doob-Meyer decomposition theorem is obtained.     

Dense Families of Selections and Finite-Dimensional Spaces

A characterization of n-dimensional spaces via continuous selections avoiding Z _n -sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem, and to obtain a new alternative proof of the Hurewicz formula. It is also shown that our selection theorem yields an easy proof of a Michael's result.     

A generalized Henstock-Stieltjes integral involving division functions

We can consider the Riemann-Stieltjes integral dg as an integral of a point function f with respect to an interval function g. We could extend it to the Henstock-Stieltjes integral. In this paper, we extend it to a generalized Stieltjes integral dg of a point function f with respect to a function g of divisions of an interval. Then we prove for this integral the standard results in the theory of integration, including the controlled convergence theorem.      

Weak Equality and Exact Sequences in H v -modules

The largest class of multivalued systems satisfying the module-like axioms is the H_v-module. H_v-modules first were introduced by Vougiouklis. In this paper we define weak equality between two subsets of an H_v-module and introduced the notion of exact sequences of H_v-modules. Also some results on the weak equality and exact sequences are given.     

A theorem concerning a product of a general class of polynomials and theH-function of several complex variables

A theorem concerning a product of a general class of polynomials and theH-function of several complex variables is given. Using this theorem certain integrals and expansion formula have been obtained. This general theorem is capable of giving a number of new, interesting and useful integrals, expansion formulae as its special cases.     

Closed graph and open mapping theorems for normed cones

A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.     

A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, η, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature.     

Value-distribution of twisted automorphic <Emphasis Type="Italic">L</Emphasis>-functions

In this paper, we prove a limit theorem for twisted with character automorphic L-functions with an increasing modulus of the character.     

On the Local Uniqueness of Solutions of Variational Inequalities Under H-Differentiability

In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C ¹ and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C ² and C ¹ nonlinear complementarity problems.     

广义强向量拟均衡问题组解的存在性

本文研究了一类集值广义强向量拟均衡问题组解的存在性问题.利用集值映射的自然拟C-凸性和集值映射的下(-C)-连续性的定义和Kakutani-Fan-Glicksberg不动点定理,在不要求锥C的对偶锥C~*具有弱*紧基的情况下,建立了该类集值广义强向量拟均衡问题组解的存在性定理.所得结果推广了该领域的相关结果.     

Mean value in invexity analysis

In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).     

On F-Implicit Generalized Vector Variational Inequalities

In this paper, we study the F-implicit generalized (weak) case for vector variational inequalities in real topological vector spaces. Both weak and strong solutions are considered. These two sets of solutions coincide whenever the mapping T is single-valued, but not set-valued. We use the Ferro minimax theorem to discuss the existence of strong solutions for F-implicit generalized vector variational inequalities.     

The (<Emphasis Type="Italic">S</Emphasis>)<Subscript>+</Subscript> condition on generalized variational inequalities

In this paper, we derive some existence results for generalized variational inequalities associated with mappings satisfying the (S)₊ condition. The relation between the (S)₊ and (S)₊¹ conditions is discussed. As an application, we also consider multivalued complementarity problems associated with mappings satisfying the (S)₊ condition, and prove a theorem to characterize the solvability of such problems in terms of exceptional families of elements.     

A solution of the Steenrod problem for G-Moore spaces

The purpose of this paper is to prove the following theorem: If G is a finite group, then every G-module is isomorphic to the homology of a G-Moore space if and only if all Sylow subgroups of G are cyclic.