Generalization of preinvex and B-vex functions

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.     

一类凸模糊映射的注记

本文讨论了一些凸模糊映射与拟凸模糊映射的性质及其在凸模糊优化的应用 .     

Pseudolinear fuzzy mappings

Two classes of fuzzy mappings, called pseudolinear and η-pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo-convex and pseudo-invex fuzzy mappings. First, some characterizations of pseudolinear and η-pseudolinear fuzzy mappings are obtained. Then, characterizations of the solution sets of pseudolinear and η-pseudolinear fuzzy programs are derived.     

广义B-凸模糊映射及其应用

提出B-E-凸模糊映射的概念,并讨论了其一些性质,得到了这一类广义B-凸模糊映射的若干刻划定理,还讨论了这一类广义B-凸模糊映射在模糊优化中的应用,并得到了和最优解有关的一些结果。     

半模糊凸模糊映射

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.     

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

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On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings

In this paper, we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings. We define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm. Our results improve and generalize many known corresponding results.     

一致凸模糊映射及其有关性质

讨论了模糊映射的一致凸性及其有关性质,给出了模糊映射为一致凸的几个判别准则,并得到了可微一致凸模糊映射在某一点达到最小值的充分条件.     

On the stability of closed-convex-valued mappings and the associated boundaries

This paper deals with the stability properties of those set-valued mappings from locally metrizable spaces to Euclidean spaces for which the images are the convex hull of their boundaries (i.e., they are closed convex sets not containing a halfspace). Examples of this class of mappings are the feasible set and the optimal set of convex optimization problems, and the solution set of convex systems, when the data are subject to perturbations. More in detail, we associate with the given set-valued mapping its corresponding boundary mapping and we analyze the transmission of the stability properties (lower and upper semicontinuity, continuity and closedness) from the given mapping to its boundary and vice versa.     

THE PARAMETRIC REPRESENTATION FOR SPIRAL-LIKE MAPPINGS OF TYPE α ON BOUNDED BALANCED PSEUDOCONVEX DOMAINS

Let Ω be a bounded balanced pseudoconvex domain in Cn that admits a plurisubhamonic defining function of class C2. The authors prove that if f is a spiral-like mapping of type α on Ω, then f can be expressed as a limiting form concerning a Schwarz mapping. Moreover, the characteristics for star-like mappings and spiral-like mappings of type α are obtained. As a direct application, the growth theorem for spiral-like mappings of type α is set up.     

严格 B -预不变凸函数

该文首先得到了严格B -预不变凸函数的一个充分条件,然后给出了严格 B -预不变凸函数的一些性质,最后得到了关于目标函数为严格 B -预不变凸函数的极小化问题的若干结果.     

Stable pseudomonotone variational inequality in reflexive Banach spaces

Stability of a generalized variational inequality with either the mapping or the set perturbed is discussed in reflexive Banach spaces, provided that the mappings are pseudomonotone in the sense of Karamardian. As a byproduct, generalized variational inequality having nonempty and bounded set is proved to be equivalent to the strictly feasibility.     

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

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Existence of Invariant Tori for Certain Weakly Reversible Mappings

In this paper, we consider certain mappings, ${\mathcal {M}}In this paper, we consider certain mappings, ℳ , sufficiently close to an integrable one, which is weakly reversible with respct to the mappings ? sufficiently close to an involution of tye (m, n), where m, n∈Z ₊ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence of a Cantor family of m-tori invariant under the reversible mappings ℳ and the reversing mapping ?. Received September 29, 1999, Accepted July 18, 2000     

On a subclass of quasi-convex mappings

A class of biholomorphic mappings named “quasi-convex mappings of type D” is introduced in the unit ball of a complex Banach space, which is the natural generalization of the convex functions in one variable. It is proved that this class of mappings is a subset of the class of “quasi-convex mappings of type A” introduced by K.A. Roper and T.J. Suffridge.     

凸模糊映射的共轭映射

本文在Goetschel和Voxman所建立的拓扑向量空间中引入了反模糊数的概念,并建立了反模糊数空间,讨论了有关的基本性质.在此基础上,引入了凸模糊映射的共轭映射的定义,并证明了凸模糊映射的共轭集合和共轭映射都是凸的.     

有限个严格压缩映像隐迭代格式的逼近

假设E为一致凸的Banach空间,对偶空间E*有Kadec-Klee性质,K为E的非空闭凸子集{Ti:i=1,2,…,N}:K→K为Browder-Petryshyn意义下的严格伪压缩映像且F=∩Ni=1F(Ti)≠0.{αn}n∞=1满足0相似文献   

Convergence and finite determination of formal CR mappings

It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds, convergence is proved e.g. under the assumption that the source is of finite type, the target does not contain a nontrivial holomorphic variety, and the mapping is finite. Finite determination (by jets of a predetermined order) of formal mappings between smooth generic submanifolds is also established.

     

严格伪压缩映像族隐格式迭代逼近不动点几何结果

对非线性算子迭代序列逼近不动点过程的几何结构进行研究,在提出并证明了一个H ilbert空间中收敛序列的钝角原理基础上,应用这个钝角原理研究了严格伪压缩映像族的隐格式迭代序列逼近公共不动点的几何结构.并证明了相应的钝角原理.这个钝角原理表述了严格伪压缩映像族的隐格式迭代序列逼近公共不动点时与公共不动点集形成了钝角关系.这个钝角关系是使用相应内积序列的上极限表示的.事实上这个钝角结果的表述形式也是一个几何变分不等式,迭代序列的极限点即是这个几何变分不等式的解.一方面这个钝角结果表述了严格伪压缩映像族公共不动点隐格式逼近的几何过程,另一方面,这个钝角结果自然是隐格式迭代序列逼近严格伪压缩映像族公共不动点的必要条件.     

Common fixed points for discontinuous mappings in fuzzy metric spaces

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.