dynamical and cohomological obstructions to extending group actions motivated by a question of ghys we study obstructions to extending group actions on the boundary partial m of a 3 manifold to a c 0 action on m among other results we show that for a 3 manifold m the s 1 times s 1 action on the boundary does not extend to a c 0 action of s 1 times s 1 via homeomorphisms that are isotopic to the identity as a discrete group on m except in the trivial case m cong d 2 times s 1

the lagrange multiplier rule in set valued optimization the known lagrange multiplier rule is extended to set valued constrained optimization problems using the contingent epiderivative as differentiability notion a necessary optimality condition for weak minimizers is derived which is also a sufficient condition under generalized convexity assumptions

scalar multiplier rules in set valued optimization in this work we establish necessary and sufficient conditions for weak minimizers of a constrained set valued optimization problem these conditions are given by means of multiplier rules formulated in terms of contingent epiderivatives of scalar set valued maps we consider that the image spaces are finite dimensional and the set valued maps are convex and stable for these conditions our results provide a scalar version of analogous existing results in the literature under weaker existence conditions moreover we prove that the multiplier rules can be computed in terms of the directional derivative of associated maps of infima

variational characterization of the contingent epiderivative abstract in this paper the existence of the contingent epiderivative of a set valued map is studied from a variational perspective we give a variational characterization of the ideal minimal of a weakly compact set as a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems when a set valued map takes values in r n we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set valued maps by applying these results we extend some existing theorems

set relations and optimality conditions in set valued maps abstract problems in set valued optimization can be solved via set optimization in this paper properties of set optimization are investigated conditions for existence of solutions are established directional derivatives are studied for set valued mappings necessary and sufficient conditions in the existence of solutions are showed with directional derivatives

existence theorems for set optimization problems abstract in this paper we consider set optimization problems by using a partial ordering based on a set relation we establish several existence results of minimal elements more general than those existing in the literature as an application we present sufficient conditions for the existence of solutions of a set valued optimization problem under some semi continuity assumption

generalized f complementarity problems in banach spaces abstract in this paper a class of generalized f complementarity problems and three classes of variational inequalities are introduced in real banach spaces and the equivalences among them are established under certain conditions several coercivity conditions are introduced for the existence of solutions of the generalized f complementarity problem under some suitable assumptions it is shown that each of these coercivity conditions is equivalent to the nonemptyness and boundedness of the solution set for the generalized f complementarity problem in infinite dimensional banach spaces and even the nonemptyness and compactness of the solution set for the generalized f complementarity problem in finite dimensional spaces the existence of least elements for the feasible set of the generalized f complementarity problem is also presented under suitable conditions

dubovitskii milyutin approach in set valued optimization by exploring the ideas around the dubovitskii milyutin approach necessary optimality conditions are given for various optimality notions in set valued optimization these optimality conditions are given by using the contingent derivative and the generalized contingent epiderivative of the objective set valued map and the set valued maps defining the constraints the notions of subgradients and scalarized subgradients for set valued maps are proposed and used to state some regularity conditions

critical point theory on partially ordered hilbert spaces we develop some abstract critical point theory in order to prove that boundary value problems like the model problem formula on a bounded domain rn 2 p 2n n 2 have infinitely many sign changing solutions uk k n which are not comparable that is uk ul and uk ul change sign for k l we also show that there are no subsolutions u such that u uk for some k and u is positive somewhere a corresponding nonexistence result applies to supersolutions related results on the existence of sign changing solutions hold for other classes of nonlinearities

scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives in this paper necessary and sufficient conditions for strict minimizers of a general vector optimization problem are given by means of different notions of graphical or epigraphical derivatives extending some existing results in the literature in first place these conditions are established by means of contingent derivatives and secondly by applying a nonconvex separation result in terms of contingent epiderivatives and hypoderivatives moreover through a variational approach a scalarization method is developed in order to obtain scalar versions of these results

equivalence of nonlinear complementarity problems and least element problems in banach lattices a class of not necessarily linear operators a v v is introduced where the banach space v and its dual v carry dual vector lattice orderings these operators called z maps generalize the n n real matrices with nonnegative off diagonal elements if a is a strictly monotone z map with certain regularity and growth conditions and if f denotes the set of all vectors v v for which v 0 and av 0 then it is shown that the complementarity problem to find v f such that 0 and the least element problem to find v f with v w for all w f have the same unique solution some other problems equivalent to these and some examples are discussed

λ c contingent derivatives of set valued maps abstract in this paper a new notion of differentiability of set valued maps is introduced based on ordered spaces techniques c lower and c upper contingent derivatives are defined conditions for c differentiability are given furthermore we show that these concepts are suitable for the formulation of optimality conditions for set valued optimization problems with set optimization criteria

vector complementarity problems with a variable ordering relation in this paper we investigate vector complementarity problems with a variable ordering relation we establish existence results of a solution of a vector complementarity problem under an inclusive type condition we obtain equivalence results among a vector complementarity problem a vector variational inequality problem and other related problems

generalized vector complementarity type problems in topological vector spaces in this paper we introduced the generalized vector variational inequality type problem and the generalized vector complementarity type problem in the setting of topological vector space by utilizing a modified version of the fan kkm theorem we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption further we prove that solution sets of both the problems are equivalent to each other under some suitable conditions the results of this paper generalize and improve several results that appeared recently in the literature

the role of directional compactness in the existence and computation of contingent epiderivatives abstract this paper underlines the role of directional compactness in the scalarization of graphical derivatives of set valued maps taking values in infinite dimensional spaces two main theorems are given the first one states the equivalence of contingent epiderivatives and w contingent epiderivatives for directionally compact maps the second main result proves a variational characterization for the contingent epiderivative of stable and directionally compact maps taking values in general image spaces extending known results in finite dimensional and reflexive banach spaces the hypotheses given are minimal as is shown by means of several examples connections of these theorems with other results of the literature are also provided

nonconvex scalarization in set optimization with set valued maps abstract the aim of this work is to obtain scalar representations of set valued optimization problems without any convexity assumption using a criterion of solution introduced by kuroiwa d kuroiwa some duality theorems of set valued optimization with natural criteria in proceedings of the international conference on nonlinear analysis and convex analysis world scientific river edge nj 1999 pp 221 228 which is based on ordered relations between sets we characterize this type of solutions by means of nonlinear scalarization the scalarizing function is a generalization of the gerstewitz s nonconvex separation function as applications of our results we give two existence theorems for set valued optimization problems

about contingent epiderivatives abstract in this paper we analyze some questions concerning the contingent epiderivative when the ordering cone is not necessarily pointed we introduce the notion of family of contingent epiderivatives we also investigate the relationship between the contingent derivative and the generalized epiderivative furthermore we give existence theorems with respect to daniell cones as a particular case we study set valued maps that take values in r n

generalized vector complementarity problem in fuzzy environment abstract this paper is devoted to introduce and study a new class of generalized vector complementarity problems gvcp for short and generalized vector variational inequalities gvvi for short in fuzzy environment under suitable conditions we prove the equivalence between gvcp and gvvi in banach spaces then without any monotonicity assumption we apply kkm technique to establish an existence theorem of solutions for gvvi finally we show that the solution set of gvcp is nonempty and closed

epidifferentiability of the map of infima in hilbert spaces this article deals with derivatives for set valued maps that take values in ordered vector spaces in particular it concerns about the relationship between the epiderivatives of a set valued map and its associated map of infima when the image space is a real separable hilbert space ordered by an orthonormal basis by using a variational technique based on a decoupling of the ordering cone into half spaces we show that both epiderivatives coincide under certain hypothesis of compactness and stability furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set valued maps

computation formulas and multiplier rules for graphical derivatives in separable banach spaces abstract in this paper we present new computation formulas for the contingent epiderivative and hypoderivative of a set valued map taking values in a banach space with a shrinking schauder basis these formulas are established in terms of the fourier coefficients and in particular in terms of the derivatives of the component maps associated with the schauder basis as an application we obtain multiplier rules for vector optimization problems in terms of the derivatives of the component maps extending classical results from smooth multiobjective optimization problems

τw contingent epiderivatives in reflexive spaces abstract in this paper we introduce a notion of the w contingent epiderivative of a set valued map by considering the weak topology in the image space we establish a chain rule formula for families of w contingent and contingent epiderivatives when the image space is reflexive and the ordering cone a half space we give conditions for the existence of the family of w contingent epiderivatives of a stable set valued map moreover we obtain an interesting formula that connects this family with the contingent epiderivative of an associated scalar set valued map finally we apply the previous results in order to establish optimality conditions for a set valued optimization problem via epiderivatives with respect to half spaces associated with the ordering cone in particular we provide a scalarization method for computing these conditions in reflexive spaces

some remarks on the existence and computation of contingent epiderivatives abstract in this paper some questions about the existence and computation of contingent epiderivatives of set valued maps are discussed a variational characterization of w contingent epiderivatives is established when the image space is a reflexive banach space moreover a representation formula for these derivatives in terms of epiderivatives of scalar maps is established for the case of a hilbert space ordered by a basis symmetrical results for contingent hypoderivatives are also provided

remarks on the cobordism group of surface diffeomorphisms in this note we sketch our computation of the group a 2 of cobordism classes of orientation preserving diffeomorphisms of closed oriented surfaces see sect 2 for precise definitions this computation was made independently and a little earlier by bonahon 2 our development follows in part the same lines extending approaches to related questions by scharleman 13 and johannson and johnson 10 who were the first to apply the characteristic manifold theory of johannson 8 and jaco and shalen 7 to questions about surface diffeomorphisms bonahon s approach depends crucially on the mostow rigidity theorem and the unpublished and as yet inaccessible hyperbolization theorem of thurston in contrast we get by with the g signature theorem in dimension two a classical formula and some number theory for this reason we have belatedly decided to publish our own approach our main contribution is a proof independent of deep three dimensional geometry that an orientation preserving periodic surface diffeomorphism which bounds as a diffeomorphism also bounds periodically cf i 2 proposition b the proof is given in sect 3 in sect 2 we develop the proof of the main calculation modulo the analysis of periodic diffeomorphisms deferred to sect 3