the influence of ss quasinormality of some subgroups on the structure of finite groups the following concept is introduced a subgroup h of the group g is said to be ss quasinormal supplement sylow quasinormal in g if h possesses a supplement b such that h permutes with every sylow subgroup of b groups with certain ss quasinormal subgroups of prime power order are studied for example fix a prime divisor p of g and a sylow p subgroup p of g let d be the smallest generator number of p and md p denote a family of maximal subgroups p1 pd of p satisfying i 1d pi p the frattini subgroup of p assume that the group g is p solvable and every member of some fixed md p is ss quasinormal in g then g is p supersolvable

solvability of variational inequalities on hilbert lattices this paper provides a systematic solvability analysis for generalized variational inequalities on separable hilbert lattices by contrast to a large part of the existing literature our approach is lattice theoretic and is not based on topological fixed point theory this allows us to establish the solvability of certain types of generalized variational inequalities without requiring the involved set valued maps be hemicontinuous or monotonic some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work and appear to have scope for applications this is illustrated by means of several applications to fixed point theory optimization and game theory

permutable products of supersoluble groups we investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups we show that the supersoluble residual is nilpotent and the fitting quotient group is metabelian these results are consequences of our main theorem which states that such a product is supersoluble when the intersection of the two factors is core free in the group

generalizations of the fkkm theorem and the ky fan minimax inequality with applications to maximal elements price equilibrium and complementarity abstract this paper generalizes the fan knaster kuratowski mazurkiewicz fkkm theorem of ky fan game theory and related topics pp 151 156 north holland amsterdam 1979 and math ann 266 1984 519 537 and the ky fan minimax inequality by introducing a class of the generalized closedness and continuity conditions which are called the transfer closedness and transfer continuities we then apply these results to prove the existence of maximal elements of binary relations under very weak assumptions we also prove the existence of price equilibrium and the complementarity problem without the continuity assumptions thus our results generalize many of the existence theorems in the literature

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

generalised quasi variational inequalities for upper semi continuous operators on non compact sets suppose that e is a topological vector space and x is a non empty subset of e let s x 2 x and t x e be two maps then the quasi variational

some new characterizations of pst groups abstract let h and b be subgroups of a finite group g such that g n g h b then we say that h is quasipermutable respectively s quasipermutable in g provided h permutes with b and with every subgroup respectively with every sylow subgroup a of b such that h a 1 in this paper we analyze the influence of s quasipermutable and quasipermutable subgroups on the structure of g as an application we give new characterizations of soluble pst groups

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

a perturbed algorithm of variational inclusions for fuzzy mappings in this paper we introduce a class of variational inclusions for fuzzy mappings and show its equivalence with a class of fixed point problems using this equivalence we develop the perturbed iterative algorithms for this class of variational inclusions further we prove the existence of solutions for the class of variational inclusions and discuss the convergence criteria for the perturbed algorithms

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

existence of solutions for vector optimization problems we define the generalized efficient solution which is more general than the weakly efficient solution for vector optimization problems and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational like inequalities for set valued maps

generalized strongly quasivariational inequalities for fuzzy mappings abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly variational inequality for fuzzy mappings and a generalized strongly complementaryty problemsfor fuzzy mappings by using the projection method

generalized bi quasi variational inequalities for quasi pseudo monotone type i operators on non compact sets in this paper the authors prove some existence results for solutions for a new class of generalized bi quasi variational inequalities gbqvi for quasi pseudo monotone type i and strongly quasi pseudo monotone type i operators defined on non compact sets in locally convex hausdorff topological vector spaces in obtaining these results on gbqvi for quasi pseudo monotone type i and strongly quasi pseudo monotone type i operators we shall use chowdhury and tan s generalized version of ky fan s minimax inequality as the main tool

x semipermutable subgroups of finite groups abstract let x be a non empty subset of a group g then we call a subgroup a of g a x semipermutable subgroup of g if a has a supplement t in g such that for every subgroup t 1 of t there exists an element x x such that a t 1 x t 1 x a in this paper we study the properties of x semipermutable subgroups in particular a new version of the famous schur zassenhaus theorem in terms of x semipermutable subgroups is given

finite groups with certain subgroups of sylow subgroups complemented abstract let g be a finite group and h a subgroup of g we say that h is complemented in g if there exists a subgroup k of g such that g h k and h k 1 for each prime p dividing the order of g let p be a sylow p subgroup of g we fix in each p a subgroup d such that 1 d p and study the structure of g under the assumption that each subgroup h of p with h d and h p d is complemented in g

the symbol grounding problem there has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling this paper describes the symbol grounding problem how can the semantic interpretation of a formal symbol system be made intrinsic to the system rather than just parasitic on the meanings in our heads how can the meanings of the meaningless symbol tokens manipulated solely on the basis of their arbitrary shapes be grounded in anything but other meaningless symbols the problem is analogous to trying to learn chinese from a chinese chinese dictionary alone a candidate solution is sketched symbolic representations must be grounded bottom up in nonsymbolic representations of two kinds 1 iconic representations which are analogs of the proximal sensory projections of distal objects and events and 2 categorical representations which are learned and innate feature detectors that pick out the invariant features of object and event categories from their sensory projections elementary symbols are the names of these object and event categories assigned on the basis of their nonsymbolic categorical representations higher order 3 symbolic representations grounded in these elementary symbols consist of symbol strings describing category membership relations e g an x is a y that is z connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations thereby connecting names to the proximal projections of the distal objects they stand for in this way connectionism can be seen as a complementary component in a hybrid nonsymbolic symbolic model of the mind rather than a rival to purely symbolic modeling such a hybrid model would not have an autonomous symbolic module however the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom up grounding of categories names in their sensory representations symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens but by the nonarbitrary shapes of the icons and category invariants in which they are grounded

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

the generalized quasi variational inequality problem over non compact sets abstract in this note we shall prove new existence results for the generalized quasi variational inequality problem which includes as particular cases all the existing generalizations of the classical variational inequality problem

a generalization of generalized quasi variational inequalities abstract the aim of this paper is to give an application of a fixed point theorem of a compact acyclic multifunction to a generalized quasi variational inequality problem in a non compact setting we present some general acyclic valued versions of several known results due to kim shih and tan

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

existence and iterative approximation of solutions of generalized mixed quasi variational like inequality problem in banach spaces in this paper some existence theorems for the mixed quasi variational like inequalities problem in a reflexive banach space are established the auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution for the mixed quasi variational like inequalities problem consequently not only the existence of theorems of the mixed quasi variational like inequalities is shown but also the convergence of iterative sequences generated by the algorithm is also proven the results proved in this paper represent an improvement of previously known results

generalized nash games and quasi variational inequalities abstract a generalized nash game is an n person noncooperative game with nondisjoint strategy sets other names for this game form include social equilibria and pseudo nash games this paper explores both the qualitative and quantitative properties of such games through the use of quasi variational inequality theory several interesting relationships between the variational and quasi variational inequality forms of this class of games are described and the practical implementation of generalized nash games are explored at length

geometric learning algorithms abstract emergent computation in the form of geometric learning is central to the development of motor and perceptual systems in biological organisms and promises to have a similar impact on emerging technologies including robotics vision speech and graphics this paper examines some of the trade offs involved in different implementation strategies focusing on the tasks of learning discrete classifications and smooth nonlinear mappings the trade offs between local and global representations are discussed a spectrum of distributed network implementations are examined and an important source of computational inefficiency is identified efficient algorithms based on k d trees and the delaunay triangulation are presented and the relevance to biological networks is discussed finally extensions of both the tasks and the implementations are given

a variational inequality approach for the determination of oligopolistic market equilibrium this paper presents an alternative approach to that by murphy sherali and soyster 13 for computing market equilibria with mathematical programming methods this approach is based upon a variational inequality representation of the problem and the use of a diagonalization relaxation algorithm

quasi variational inequalities with non compact sets in this paper we first generalize a foundational quasi variational inequality theorem 3 which plays a key role throughout this paper by relaxing the compactness condition then we set up general forms of generalized quasi variational inequalities and obtain a series of existence theorems without the compactness assumption also since many other quasi variational inequalities in the literature are special cases of ours they can be generalized by our results

iterative algorithm for completely generalized set valued strongly nonlinear mixed variational like inequalities a class of completely generalized set valued strongly nonlinear mixed variational likeinequalities is introduced the auxiliary principle technique is extended to study this new class of mixed variational like inequalities the existence of a solution of the auxiliary problem for this new class of mixed variational like inequalities is shown the iterative algorithm for this new class of mixed variational like inequalities is given by virtue of this existence result moreover the existence of a solution of this new class of mixed variational like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown the convergence criteria are different from some early and recent ones presented in the literature

on the general variational inequality abstract in this paper we investigate the general variational inequality which extends the classical variational inequality in finite dimensional spaces necessary and sufficient conditions for the existence of a solution of this problem are obtained some existence results are derived using the fixed point theory uniqueness of the solution is also discussed application of these existence results to the implicit complementarity problem is given

approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions the purpose of this paper is to investigate the convergence of general approximate proximal algorithm resp general bregman function based approximate proximal algorithm for solving the generalized variational inequality problem for short gvi t w where t is a multifunction the general approximate proximal algorithm resp general bregman function based approximate proximal algorithm is to define new approximating subproblems on the domains w email protected email protected n 1 2 which form a general approximate proximate point scheme resp a general bregman function based approximate proximate point scheme for solving gvi t w it is shown that if t is either relaxed a pseudomonotone or pseudomonotone then the general approximate proximal point scheme resp general bregman function based approximate proximal point scheme generates a sequence which converges weakly to a solution of gvi t w under quite mild conditions

weakly c permutable subgroups of finite groups abstract a subgroup h of a group g is called weakly c permutable in g if there exists a subgroup t of g such that g h t and h t is completely c permutable in g in this paper we obtain some results about the weakly c permutable subgroups and use them to determine the structures of some groups in particular we give some new characterizations of supersolvability and p nilpotency of a group and more general a group belonging to a given formation of finite groups by using the weakly c permutability of some primary subgroups as application we generalize a series of known results

multivalued s 1 operators and generalized variational inequalities abstract in this paper we derive some new existence results for the generalized variational inequalities by introducing multivalued s 1 operators applications to nonlinear inequalities and the generalized complementarity problem are given

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

the generalized vector quasi variational like inequalities abstract in this paper we introduce and study a class of generalized vector quasi variational like inequality problem gvqvlip involving set valued mappings with certain monotonicity by employing the scalarization technique several existence results for solutions of the gvqvlip are established under noncompact setting in topological vector spaces these new existence results improve unify and generalize many known results for scalar and vector variational inequalities in recent literature

existence of pareto equilibria for constrained multiobjective games in h space abstract in this paper we introduce and study a new class of constrained multiobjective games in h spaces without linear structure an existence theorem of solutions for quasi equilibrium problems is first proved in noncompact h spaces then as applications of the quasi equilibrium existence theorem several existence theorems of weighted nash equilibria and pareto equilibria for the constrained multiobjective games are established in noncompact h spaces these theorem improve unify and generalize the corresponding results of the multiobjective games in recent literature

the maximum theorem and the existence of nash equilibrium of generalized games without lower semicontinuities abstract in this paper we generalize berge s maximum theorem to the case where the payoff utility functions and the feasible action correspondences are not lower semicontinuous the condition we introduced is called the feasible path transfer lower semicontinuity in short fpt l s c by applying our maximum theorem to game theory and economics we are able to prove the existence of equilibrium for the generalized games the so called abstract economics and nash equilibrium for games where the payoff functions and the feasible strategy correspondences are not lower semicontinuous thus the existence theorems given in this paper generalize many existence theorems on nash equilibrium and equilibrium for the generalized games in the literature

on generalized u hypercentral subgroups of a finite group abstract we give some conditions under which a normal subgroup of a finite group g is contained in the intersection of all maximal supersoluble subgroups of g

a note on the existence of traffic equilibria this note presents an alternative proof of the existence of a solution to the network equilibrium problem which is based on the recent work in complementarity theory by t smith 11

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity we propose an approximate proximal algorithm for solving generalized variational inequalities in hilbert space extension to bregman function based approximate proximal algorithm is also discussed weak convergence of these two algorithms are established under the paramonotonicity and pseudomonotonicity assumptions of the operators

on c supplemented subgroups of finite groups abstract let g be a finite group a subgroup h of g is said to be c supplemented in g if there exists a subgroup k of g such that g h k and h k h g where h g g g h g is the largest normal subgroup of g contained in h we investigate the structure of g under the assumption that some families of subgroups of g are c supplemented in g

generalized variational inequalities and generalized quasi variational inequalities abstract a very general minimax inequality is first established three generalized variational inequalities are then derived which improve those obtained by tan and browder by applying a fixed point theorem of himmelberg two generalized quasi variational inequalities are also proved one of which generalizes those of shih tan to the non compact case with much weaker hypotheses and in a more general setting

existence of solutions for lower semicontinuous quasi equilibrium problems in this paper we deal with the following quasi equilibrium problem given a nonempty subset c of a topological vector space x a nonempty set d two functions t c d f x d r and a multifunction s c 2x find x x such that x c x s x and f x tx f x tx for all x s x such a problem recently introduced in 1 extends and unifies several variational inequality problems generalized complementarity problems and nash equilibrium problems we prove several existence results in which the upper semicontinuity of the multifunction s is not assumed

finite groups with generalized ore supplement conditions for primary subgroups abstract we associate with every group g a set g of subgroups of g with 1 g if h g then we say that h is a subgroup of g if g g for each epimorphism g g then we say that is a subgroup functor we say also that a subgroup functor is hereditary provided h e whenever h e g and h g regular provided for any group g whenever h g is a p group and n is a minimal normal subgroup of g then g n g h n is a power of p regular respectively quasiregular provided for any primitive group g whenever h g is a p group and n is a respectively abelian minimal normal subgroup of g then g n g h n is a power of p let k h be subgroups of g and a subgroup functor then we say that the pair k h satisfies the f supplement condition in g if g has a subgroup t such that h t g and h t k z f t h is f supplemented in g if for some subgroup s of g contained in h the pair s h satisfies the f supplement condition in g where g g h g and h h h g in this paper we study the structure of a group g under the condition that some primary subgroups of g are f supplemented in g in particular we prove the following result theorem a let f be a saturated formation containing the class u of all supersoluble groups e a normal subgroup of g with g e f x e or x f e and a regular or hereditary regular subgroup functor suppose that every subgroup of g contained in x is subnormally embedded in g if every maximal subgroup of every non cyclic sylow subgroup of x is u supplemented in g then g f moreover in the case when is regular then every chief factor of g below e is cyclic the results in this paper not only cover and unify a long list of some known results but also cause a wide series of new results

generalized bi quasi variational inequalities abstract let e f be hausdorff topological vector spaces over the field which is either the real field or the complex field let f e be a bilinear functional and let x be a non empty subset of e given a multi valued map s x 2x and two multi valued maps m t x 2f the generalized bi quasi variational inequality gbqvi problem is to find a point y x such that y s y and inf w t y re w y x 0 for all x s y and for all m y in this paper two general existence theorems on solutions of gbqvis are obtained which simultaneously unify sharpen and extend existence theorems for multi valued versions of hartman stampacchia variational inequalities proved by browder and by shih and tan variational inequalities due to browder existence theorems for generalized quasi variational inequalities achieved by shih and tan theorems for monotone operators obtained by debrunner and flor fan and browder and the fan glicksberg fixed point theorem

generalized variational and quasi variational inequalities with discontinuous operators abstract we study the existence of solutions to generalized variational and generalized quasi variational inequalities with discontinuous operators we obtain results which generalize and extend previously known theorems we also compare our new continuity condition on the operator in the variational inequality to previously used continuity conditions we then apply our results to generalized variational inequalities which involve pseudo monotone operators

existence theorems of solutions for generalized quasi variational inequalities a minimax theorem and a section theorem in the spaces without linear structure in this paper by using particular techniques two existence theorems of solutions for generalized quasi variational inequalities a minimax theorem and a section theorem in the spaces without linear structure are established and finally a new coincidence theorem in locally convex spaces is obtained

vector quasivariational inequalities for fuzzy mappings ii abstract this paper is devoted to study the vector variational inequalities for fuzzy mappings by using the fan browder fixed point theorem the selection theorem of yannelis prabhakar 13 and the scalarization method of luc 9 10 some existence theorems for our inequalities are proved

existence of solutions for quasi equilibrium problems in noncompact topological spaces abstract in this paper a new fan browder type fixed point theorem is proved under noncompact setting of general topological spaces by applying the fixed point theorem several new existence theorems of solutions for quasi equilibrium problems are proved under noncompact setting of topological spaces these theorems improve and generalize a number of important known results in literature

generalized quasi variational like inequality problem this paper gives some very general results on the generalized quasi variational like inequality problem since the problem includes all the existing extensions of the classical variational inequality problem as special cases our existence theorems extend the previous results in the literature by relaxing both continuity and concavity of the functional the approach adopted in this paper is based on continuous selection type arguments and thus is quite different from the berge maximum theorem or hahn banach theorem approach used in the literature

variational and generalized variational inequalities with discontinuous mappings abstract in this paper we derive several existence results for the variational and the generalized variational inequality problems where the mappings under consideration need not have any continuity properties uniqueness of the solution of the generalized variational inequality problem is also investigated as a by product we obtain several existence and uniqueness results for the generalized complementarity problem applications to minimization problems with generalized convex functions are considered

an application of a browder type fixed point theorem to generalized variational inequalities the purpose of this paper is to provide an application of a non compact version due to park of browder s fixed point theorem to generalized variational inequalities in a non compact setting we establish a fairly general existence theorem on a generalized variational inequality using the result of park our main result is not only a strict generalization of ding and tan s result without assuming any continuity of given functions but also a purely infinite dimensional version of recent results of yao and guo as an immediate consequence we obtain an extension of a result of browder concerned with generalized variational inequalities without assuming the local convexity of the underlying topological vector space

a further generalization of yannelis prabhakar s continuous selection theorem and its applications abstract in this article we first prove one improved version of the yannelis prabhakar continuous selection theorem and next as its applications a fixed point theorem in noncompact product spaces a nonempty intersection theorem some existence theorems of solutions for the generalized quasi variational inequalities and some equilibrium existence theorems for the abstract economies are given

system of coincidence theorems with applications in this paper we establish systems of coincidence theorems from which solution of system of inequalities and system of minimax theorems was established in this paper

on the generalized quasi variational inequality problems the purpose of this paper is to study the existence problem of solutions for some kinds of abstract generalized quasi variational inequality problems by using a new kind of fixed point approach

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

the theory and practice of bayesian image labeling integrating disparate sources of information has been recognized as one of the keys to the success of general purpose vision systems image clues such as shading texture stereo disparities and image flows provide uncertain local and incomplete information about the three dimensional scene spatial a priori knowledge plays the role of filling in missing information and smoothing out noise this thesis proposes a solution to the longstanding open problem of visual integration it reports a framework based on bayesian probability theory for computing an intermediate representation of the scene from disparate sources of information the computation is formulated as a labeling problem local visual observations for each image entity are reported as label likelihoods they are combined consistently and coherently on hierarchically structured label trees with a new computationally simple procedure the pooled label likelihoods are fused with the a priori spatial knowledge encoded as markov random fields mrf s the a posteriori distribution of the labelings are thus derived in a bayesian formalism a new inference method highest confidence first hcf estimation is used to infer a unique labeling from the a posteriori distribution unlike previous inference methods based on the mrf formalism hcf is computationally efficient and predictable while meeting the principles of graceful degradation and least commitment the results of the inference process are consistent with both observable evidence and a priori knowledge the effectiveness of the approach is demonstrated with experiments on two image analysis problems intensity edge detection and surface reconstruction for edge detection likelihood outputs from a set of local edge operators are integrated with a priori knowledge represented as an mrf probability distribution for surface reconstruction intensity information is integrated with sparse depth measurements and a priori knowledge coupled mrf s provide a unified treatment of surface reconstruction and segmentation and an extension of hcf implements a solution method experiments using real image and depth data yield robust results the framework can also be generalized to higher level vision problems as well as to other domains

generalized vector variational inequalities with star pseudomonotone and discontinuous operators abstract it is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems by using the ky fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star pseudomonotone operators are involved our results can be applied to the study of the existence of solutions of vector optimal problems some examples are given and analyzed

a general theorem of complementarity for the implicit gqvi problem abstract in this paper we prove a basic theory of complementarity for the implicit generalized quasi variational inequality problem our result widely extends many known results established in the literature an application to the quasi equilibrium problem is also given

a class of nonconvex functions and pre variational inequalities abstract a class of nonconvex functions is introduced called semi preinvex function which includes the classes of preinvex functions and arc connected convex functions the fritz john conditions of the mathematical programming problem are derived for these kinds of functions the pre variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions the type i function related to unconstrained problems is given as an equivalent form of the pre variational inequality existence theorems for the solution of the pre variational inequality are also proved

an existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators abstract this paper gives a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite dimensional space which is c pseudomonotone in the sense of inoan and kolumban d inoan j kolumban on pseudomonotone set valued mappings nonlinear analysis 68 2008 47 53 but which may not be upper semicontinuous on finite dimensional subspaces the proof of the theorem provides a new technique which reduces infinite variational inequality problems to finite ones two examples are given and analyzed to illustrate the theorem moreover an example is presented to show that the c pseudomonotonicity of the operator cannot be omitted in the theorem

c normality of groups and its properties we introduce a new normality in a finite group called c normality we investigate the influence of c normal subgroups on the structure of finite groups in this paper we present some necessary and sufficient conditions for a group to be p nilpotent p supersolvable and supersolvable our results unify and generalize some related ones

fixed point and maximal element theorems with applications to abstract economies and minimax inequalities in this paper we establish some fixed point theorems for a family of multivalued maps under mild conditions by using our fixed point theorems we derive some maximal element theorems for a particular family of multivalued maps namely the condensing multivalued maps as applications of our results we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences further applications of our results are also given to minimax inequalities for a family of functions

fixed point theorems with an application in generalized games abstract the purpose of this paper is to introduce several fixed point theorems on h space and to give an existence theorem of equilibrium points in generalized games

generalized quasi variational inequalities with non compact sets in this paper we will present several results concerning generalized quasi variational inequalities with non compact sets at first we generalize foundational quasi variational inequalities which play a key role throughout this paper by relaxing the compactness condition several generalized quasi variational inequalities can be extended by our results

subgroups permutable with all sylow subgroups fix a finite group g whenever s is a nonempty set of subgroups of g let sh denote the set of all subgroups h of g permutable with all s g s h so that the complex product hs s sh is their join it is obvious that s is closed with respect to joins in case s s syl g is the set of all sylow subgroups of g for all primes it is also closed with respect to intersec w x h tions kegel 4 so that syl g is a lattice the present paper may be seen as continuation of kegel s work to be more precise it aims to continue the first part of his work the second one being completed by w x kleidman 5 h syl g is the full subgroup lattice of g precisely when g g n is nilpotent the formation n of nilpotent groups will play a central role in general as usual we denote by g the nilpotent residual of g for subgroups h and k of g we write h s f h x and h k s k x g k 2 x x h x g k for the k core and the k closure of h respectively h s y1 x hx h k h suppose h g syl g then h and h do belong to syl g for all k n k but h usually does not nor does it the commutator group h9 nor the centre z h on the other hand we know that there is a unique subgroup of h minimal subject to containing h n and belonging to h syl g this is always a normal subgroup of g

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

a noncompact generalized quasi variational inequality by applying a fixed point theorem of yannelis and prabhakar a generalized quasi variational inequality is proved on a noncompact convex subset of a locally convex hausdorff topological vector space

a basic theorem of complementarity for the generalized variational like inequality problem abstract in this paper a basic theorem of complementarity is established for generalized variational like inequality problems introduced by parida and sen some existence results for both generalized variational inequality and complementarity problems are established by employing this basic theorem of complementarity in particular some sets of conditions that are normally satisfied by a nonsolvable generalized complementarity problem are investigated

generalized quasi variational inequalities in locally convex topological vector spaces abstract let e be a hausdorff topological vector space and x e an arbitrary nonempty set denote by e the dual space of e and the pairing between e and e by w x for w e and x e given a point to set map s x 2x and a point to set map t x 2e the generalized quasi variational inequality problem gqvi is to find a point y s y and a point u t y such that re u y x 0 for all x s y by using the ky fan minimax principle or its generalized version as a tool some general theorems on solutions of the gqvi in locally convex hausdorff topological vector spaces are obtained which include a fixed point theorem due to ky fan and i l glicksberg and two different multivalued versions of the hartman stampacchia variational inequality

iterative algorithm for finding approximate solutions to completely generalized strongly quasivariational inequalities for fuzzy mappings in this paper we construct a new iterative algorithm which includes many known algorithms as special cases to solve variational inequalities and quasivariational inequalities for fuzzy mappings further we prove the convergence of the iterative sequences generated by this algorithm our results are the extension and improvements of the earlier and recent results in this field

quasiequilibrium problem in h spaces in the present paper we study the quasiequilibrium problem and generalized quasiequilibrium problem of generalized quasi variational inequality in h spaces by a new method some new equilibrium existence theorems are given our results are different from corresponding given results or contain some recent results as their special cases c 2003 elsevier science ltd all rights reserved

on weakly s permutable subgroups of finite groups abstract let g be a finite group h a subgroup of g and h s g the subgroup of h generated by all those subgroups of h which are s permutable in g then we say that h is weakly s permutable in g if g has a subnormal subgroup t such that h t g and t h h s g we fix in every non cyclic sylow subgroup p of g a subgroup d satisfying 1 d p and study the structure of g under the assumption that all subgroups h with h d are weakly s permutable in g

generalized games and non compact quasi variational inequalities abstract in this paper by developing an approximation approach which is originally due to tuleca in 1986 we prove the existence of equilibria for generalized games in which constraint mappings correspondences are lower resp upper semicontinuous instead of having lower resp upper open sections or open graphs in infinite dimensional topological spaces then existence theorems of solutions for quasi variational inequalities and non compact generalized quasi variational inequalities are also established finally existence theorems of constrained games with non compact strategy sets are derived our results unify and generalize many well known results given in the existing literature in particular we answer the question raised by yannelis and prabhakar in 1983 in the affirmative under more weaker conditions