ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.

On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

A new bilevel generalized mixed equilibrium problem （BGMEP） involving generalized mixed variational-like inequality problems （GMVLIPs） is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem （AGMEP） is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.

An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

EXISTENCE OF SOLUTIONS FOR GENERALIZEDQUASI-VARIATIONAL-LIKE INEQUALITIES

In this paper, some existence theorems of solutions for a class of generalized quasi-variational-like inequalities with discontinuous mappings ape proved under paracompact setting in topological vector spaces. These theorems unify, improve and generalize many recent results.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems （GVVTIP） are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and general- ized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP axe established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.

Generalized Bi quasi variational Inequalities in Locally Convex Topological Vector Spaces

In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].

The Impact of Finance Development on the Income Inequality Between the Urban and the Rural： Evidence From Henan Province in China

Finance is one important factor to promote economic development. Meanwhile, it also has a dubious effect on income inequality in accordance with the prior literatures. In order to promote economic development, most of China’s governments provide many policies to boost financial development. However, these policies should also be evaluated with its impact on the income inequality. As one important province in China, Henan also wants to have a rapid economic development with policies on financial development. Therefore, this paper uses the vector autoregressive model to detect the impact of financial development on income inequality between the urban and the rural, and the results suggest one positive impulse on financial development would cause income inequality to be increased immediately, but to be decreased after the fourth period. Thus, Henan’s policies on financial development would achieve the goal to promote economic development without the detrimental effect on income inequality.

向量值多线性奇异积分算子的加权Sharp不等式

利用不等式、原子分解性质研究了向量值多线性算子,证明了某些向量值多线性奇异积分算子的一个加权Sharp不等式,并利用此不等式得到了该向量值多线性算子的加权L^(p)型不等式和L log L型不等式。

Generalized Vector Quasi-Variational-Like Inequalities without Monotonity and Compactness

In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.

QUASI-VARIATIONAL INEQUALITIES AND SOCIAL EQUILIBRIUM

A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilibria ofmetagames are showed which improve and extend the recent results of Kaczynski-Zeidan and Aubin.

Two-Parameter Vector-Valued Martingales and Geometrical Properties of Banach Spaces

We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.

HARDY'S INEQUALITIES WITH MAXIMIZERS FOR W^(1,p) FUNCTIONS ON BOUNDED STAR DOMAINS

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W^(1,p) functions on bounded star domains. Our results are not obtainable from the classical inequalities for W_0^(1,p) functions. Unlike in W_0^(1,p),our inequalities admit maximizers that we describe explicitly.

A Fixed Point Theorem and Some Generalized Ky Fan's Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.

Generalized Quasi Variational-Type Inequalities

In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.