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1.
Generalized B-vex functions and generalized B-vex programming   总被引:21,自引:0,他引:21  
A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319. The second author is grateful to the Faculty of Management, University of Manitoba for the financial support provided for her visit. The authors are thankful to Prof. R. N. Kaul, Department of Mathematics, Delhi University for his constructive criticism of the paper.  相似文献
2.
On vector variational inequalities   总被引:17,自引:0,他引:17  
In this paper, we introduce a general form of a vector variational inequality and prove the existence of its solutions with and without convexity assumptions.  相似文献
3.
Generalization of preinvex and B-vex functions   总被引:17,自引:0,他引:17  
A class of functions called B-preinvex functions is introduced by relaxing the definitions of preinvex and B-vex functions. Examples are given to show that there exist functions which are B-preinvex but not preinvex or B-vex or quasipreinvex. Some of the properties of B-preinvex functions are obtained.The contribution of this author was made partially at University of Manitoba and partially at St. Lawrence University during the summer of 1990. Support for the visit to St. Lawrence University was made possible under the GTE/SLU Visiting Scholars Grant.  相似文献
4.
An existence result for the generalized vector equilibrium problem   总被引:16,自引:0,他引:16  
In this paper, we prove an existence result for the generalized vector equilibrium problem by using Fan-Browder type fixed-point theorem due to [1].  相似文献
5.
Toroidal Lie algebras and vertex representations   总被引:15,自引:0,他引:15  
The paper describes the theory of the toroidal Lie algebra, i.e. the Lie algebra of polynomial maps of a complex torus ××× into a finite-dimensional simple Lie algebra g. We describe the universal central extension t of this algebra and give an abstract presentation for it in terms of generators and relations involving the extended Cartan matrix of g. Using this presentation and vertex operators we obtain a large class of integrable indecomposable representations of t in the case that g is of type A, D, or E. The submodule structure of these indecomposable modules is described in terms of the ideal structure of a suitable commutative associative algebra.To Professor J. Tits for his sixtieth birthday  相似文献
6.
Iterative Schemes for Solving Mixed Variational-Like Inequalities   总被引:14,自引:0,他引:14  
In the present paper, we introduce the concept of -cocoercivity of a map and develop some iterative schemes for finding the approximate solutions of mixed variational-like inequalities. We use the concept of -cocoercivity to prove the convergence of the approximate solutions to the exact solution of mixed variational-like inequalities.  相似文献
7.
8.
Semicontinuity and Quasiconvex Functions   总被引:11,自引:0,他引:11  
Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.  相似文献
9.
S. Ghosh 《Semigroup Forum》1999,59(1):106-120
E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi [2] in the case of Boolean semirings.  相似文献
10.
The system of generalized vector equilibrium problems with applications   总被引:8,自引:0,他引:8  
In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.  相似文献
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