KKM Theorems on FC-spaces with Their Applications to Variational Inequalities

A new concept of finitely continuous topological spaces （in short, FC-space） without convexity structure and linear structure was introduced. Some KKM type theorems in noncompact FC-spaces were obtained, and from which, some section theorems and wriational inequality theorems were proved under much weak assumptions. Our results improve and generalize the corresponding conclusions in recent literature.     

New systems of generalized quasi-variational inclusions in FC-spaces and applications

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.     

Generalized KKM-type theorems for weakly generalized KKM mapping with some applications

In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.     

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint corre- spondences are proved in FC-spaces.By using these equilibrium existence theorems,some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces.These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.     

Laws of large numbers of negatively correlated random variables for capacities

Our aim is to present some limit theorems for capacities.We consider a sequence of pairwise negatively correlated random variables.We obtain laws of large numbers for upper probabilities and 2-alternating capacities,using some results in the classical probability theory and a non-additive version of Chebyshev’s inequality and Boral-Contelli lemma for capacities.     

Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

In this work, using an analogue of Sadovskii＇s fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F（x） =μx, （μ≥1） for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].     

The Theory of Finite Models without Equal Sign

In this paper, it is the first time ever to suggest that we study the model theory of all finite structures and to put the equal sign in the same situtation as the other relations. Using formulas of infinite lengths we obtain new theorems for the preservation of model extensions, submodels, model homomorphisms and inverse homomorphisms. These kinds of theorems were discussed in Chang and Keisler＇s Model Theory, systematically for general models, but Gurevich obtained some different theorems in this direction for finite models. In our paper the old theorems manage to survive in the finite model theory. There are some differences between into homomorphisms and onto homomorphisms in preservation theorems too. We also study reduced models and minimum models. The characterization sentence of a model is given, which derives a general result for any theory T to be equivalent to a set of existential-universal sentences. Some results about completeness and model completeness are also given.     

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.     

Montel-Type Theorems in Several Complex Variables with Continuously Moving Targets

The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into p^N （C） for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results.     

ON APPROXIMATION PROPERTIES OF NON-CONVOLUTION TYPE NONLINEAR INTEGRAL OPERATORS-Dedicated to Professor Paul L. Butzer on his 80th Birthday

In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]     

Stampacchia generalized vector quasi-equilibrium problem with set-valued mapping

In this paper, the solvability of Stampacchia generalized vector quasi-equilibrium problem (in short, GVQEP) with set-valued mapping is studied. By using continuous selection theorem and fixed point theorems, some existence theorems for (GVQEP) are obtained without any monotonicity assumption. These theorems unify and improve some results in the recent references.     

Edelstein's method and fixed point theorems for some generalized nonexpansive mappings

A new condition for mappings, called condition (C), which is more general than nonexpansiveness, was recently introduced by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. Following the idea of Kirk and Massa Theorem in [W.A. Kirk, S. Massa, Remarks on asymptotic and Chebyshev centers, Houston J. Math. 16 (1990) 364-375], we prove a fixed point theorem for mappings with condition (C) on a Banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact. This covers a result obtained by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. We also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of Banach spaces satisfying property (D). Consequently, we extend the results in [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] to many other Banach spaces.     

Fixed point theory for generalized contractions in cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949].     

Existence of solutions for elliptic equations with discontinuous nonlinearities strong resonance at infinity

In the present paper, our main purposes are to study nonlinear elliptic equations with strong resonance at infinity. Some existence theorems for nontrivial solutions are obtained by using some nonsmooth critical point theorems in [N. C. Kourogenis, N. S. Papageorgiou, Nonsmooth critical point theory and Nonlinear elliptic equations at resonance, J. Austral. Math Soc. (Ser. A) 69 (2000) 245–271]. The two of our theorems generalize Theorems 0.1 and 5.2 in [P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. TMA 7 (1983) 981–1012] to nonsmooth cases. Another theorem is new even if for the smooth case.     

The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces

In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.     

Sulla convergenza delle serie reali a termini non negativi

In this paper some necessary and sufficient conditions are given for convergence of a series with non-negative terms. As a particular case, one finds again the well-known ratio-test for convergence of series with positive terms; in such a connection, some observations are made of didactical interest. Finally, some relations are emphasiged concerning theorems of convergence for real series (here obtained) and fixed point theorems already known.     

Are there free groups in division rings?

The following conjecture is investigated: a noncentral subnormal subgroup of the multiplicative group of a division ring contains a noncyclic free subgroup. Special cases are proved, entailing several known commutativity theorems. Also a new framework is presented for some kinds of commutativity theorems, based on the existence of (group) words for which one can always find an appropriate substitution by elements of such a subnormal subgroup that yields a noncentral element. Several families of such words are given; one gets commutativity theorems imposing some restrictions (like periodicity) to the image of these words.     

The Study of KKM Theorems With Applications to Vector Equilibrium Problems and Implict Vector Variational Inequalities Problems

In this paper, we establish some equivalence relations between coincidence theorems and KKM-type theorems. We also obtain some new coincidence theorems and fixed point theorems. Applying the KKM-type theorems we obtain the existence theorems of generalized vector equilibrium problems. From these results, some existence theorems of generalized vector implicit variational inequality problems are established in this paper.     

乘积G-凸空间内的非空交定理和广义矢量平衡问题组

利用作者在G-凸空间内对集值映象簇得到的一个极大元存在性定理,在非紧乘积G-空间内,对集值映象簇建立了某些新的非空交定理．作为应用, 在非紧乘积G-凸空间内, 对广义矢量平衡问题组证明了一些平衡存在性定理．这些定理统一、改进和推广了文献中一些重要的已知结果．     

Metrizability of spaces and weak base g-functions

In this paper, we give some metrization theorems and characterize some generalized metric spaces in terms of (weak base) g-functions. And we give quick proofs of two theorems in [Topology Appl. 91 (1999) 71].