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.     

Generalization of preinvex and B-vex fuzzy mappings

A class of fuzzy mappings, called B-preinvex, and strictly B-preinvex fuzzy mappings, is introduced by relaxing the definition of preinvexity of a fuzzy mapping. Similarly, based on a notion of differentiability of fuzzy mappings different from the usual one, the class of pseudo-B-vex, B-invex, and pseudo-B-invex fuzzy mappings is defined as a generalization of pseudo-convex, invex, and pseudo-invex fuzzy mappings. We prove that a strictly B-vex, or B-preinvex fuzzy mapping has at most one global minimum point, and that the class of B-vex fuzzy mappings forms a subset of the class of quasi-convex fuzzy mappings. B-vex (resp. B-preinvex) fuzzy mappings satisfy most of the basic properties of convex (resp. preinvex) fuzzy mappings. In addition characterizations and sufficient optimality conditions are obtained for B-vex and B-preinvex fuzzy mappings.     

On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings

We investigate some inequalities connected with the Hyers-Ulam stability of three functional equations, which have a solution of the form φ=a+q, where a is an additive mapping and q is a quadratic one.     

On the stability of iterative approximations to fixed points of nonexpansive mappings

We study iterative retraction approximations to fixed points of the nonexpansive self-mapping given on the closed convex set G in a Banach space B. The conditions which guarantee weak and strong convergence and stability of these approximations with respect to perturbations of both operator A and constraint set G are considered. The results of this paper are new even in a Hilbert space for the iterative projection approximations.     

Sufficient conditions for the stability of the karush- kuhn - tucker point set in quadratic programming

We obtain some conditions under which a small perturbation in the data of a quadratic programming problem can yield only a small change in its Karush-Kuhn-Tucker point set. Convexity of the objective function and boundedness of the constraint set are not assumed. The obtained results are illustrated by several examples     

On the dilatation of extremal quasiconformal mappings of polygons

A polygon P _N is the unit disk with distinguished boundary points, . An extremal quasiconformal mapping maps each polygon inscribed in onto a polygon inscribed in . Let f _N be the extremal quasiconformal mapping of P _N onto P' _N. Let K _N be its dilatation and let K ₀ be the maximal dilatation of f ₀. Then, evidently . The problem is, when equality holds. This is completely answered, if f ₀ does not have any essential boundary points. For quadrilaterals Q and Q' = f ₀ (Q) the problem is sup(M'/M) = K ₀, with M and M' the moduli of Q and Q' respectively. Received: December 23, 1997     

On the stability problem for a mixed type of quartic and quadratic functional equation

Let E₁ and E₂ be real linear spaces. In this paper, we determine the general solution for a mixed type functional equation of a quartic and a quadratic mapping f:E₁→E₂,

     

Quasiconvex functions and null Lagrangians in the stability problems of classes of mappings

We obtain stability theorems for classes of solutions to the differential equations constructed by means of quasiconvex functions and null Lagrangians.     

On the uniqueness problem of harmonic quasiconformal mappings

In this paper, we give an affirmative answer to Sheretov's problem on the uniqueness of harmonic mappings and improve the unique minimal mapping theorem of Reich and Strebel. Meanwhile, we also solve a problem posed by Reich and obtain the uniqueness theorem on related weight functions.

     

On the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings

Let X be a normed linear space and let S and T be multi-valued mappings of X into a family of closed, not necessarily compact subsets of X. In this paper some results on the convergence of the Ishikawa iterates associated with a pair S, T which satisfy the condition (8) below, are obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the stability of the solution mapping for parametric traffic network problems

In this paper, we introduce the parametric traffic network problems. Afterward, a key hypothesis is introduced by virtue of a parametric gap function to considered problems, and we prove that this hypothesis is not only sufficient but also necessary for the Hausdorff lower semicontinuity and Hausdorff continuity of the solution mapping for parametric traffic network problems.     

An optimization result for set-valued mappings and a stability property in vector problems with constraints

First, we prove an existence result relative to minimal points of set-valued mappings. Then, conditions about the upper and lower semicontinuity of constraint sets defined through set-valued mappings are given. Finally, a stability result relative to vector problems with abstract constraints is proved.The author thanks the referee for helpful comments on the first version of this paper.     

Existence and stability of periodic solutions for parabolic systems with time delays

This paper is concerned with the existence and stability time-periodic solutions for a class of coupled parabolic equations with time delay, and time delays may appear in the nonlinear reaction functions. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement. Our approach to the problem is by the method of upper and lower solution and using Schauder fixed point theorem. Some methods for proving the stability of the periodic solution are also given. The results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system. Finally, a model arising from chemistry is used to illustrate the obtained results.     

Effective results on compositions of nonexpansive mappings

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of (r,δ)$(r,\delta )$-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing.     

Epi and coepi-analysis of one class of vector-valued mappings

This article deals with a new characterization of lower semicontinuity of vector-valued mappings in normed spaces. We study the link between the lower semicontinuity property of vector-valued mappings and the topological properties of their epigraphs and coepigraphs, respectively. We show that if the objective space is partially ordered by a pointed cone with nonempty interior, then coepigraphs are stable with respect to the procedure of their closure and, moreover, the locally semicompact vector-valued mappings with closed coepigraphs are lower semicontinuous. Using these results we propose some regularization schemes for vector-valued functions. In the case when there are no assumptions on the topological interior of the ordering cone, we introduce a new concept of lower semicontinuity for vector-valued mappings, the so-called epi-lower semicontinuity, which is closely related to the closedness of epigraphs of such mappings, and study their main properties. All principal notions and assertions are illustrated by numerous examples.     

On the stable containment of two sets

This paper studies the stability of the set containment problem. Given two non-empty sets in the Euclidean space which are the solution sets of two systems of (possibly infinite) inequalities, the Farkas type results allow to decide whether one of the two sets is contained or not in the other one (which constitutes the so-called containment problem). In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the two sets is preserved by sufficiently small perturbations or not. This paper deals with this stability problem as a particular case of the maintaining of the relative position of the images of two set-valued mappings; first for general set-valued mappings and second for solution sets mappings of convex and linear systems. Thus the results in this paper could be useful in the postoptimal analysis of optimization problems with inclusion constraints.      

一维奇异p-Laplace方程的上下解方法[英文]

本文讨论了一维奇异 p Laplace方程( φp( y′) )′+ q(t) f(t,y) =0 ,0 相似文献