an iterative scheme for a class of quasi variational inequalities an iterative scheme is given to obtain the approximate solution of a class of quasi variational inequalities it is shown that the approximate solution obtained by the iterative scheme converges strongly in the hilbert space to the exact solution as a special case we obtain the corresponding iterative scheme for variational inequalities

proximal point algorithm for generalized multivalued nonlinear quasi variational like inclusions in banach spaces in this paper we define a new notion of j h proximal mapping for a nonconvex lower semicontinuous h subdifferentiable proper functional in banach spaces the existence and lipschitz continuity of j h proximal mapping of a lower semicontinuous h subdifferentiable proper functional are proved by applying this notion we introduce and study generalized multivalued nonlinear quasi variational like inclusions in reflexive banach spaces and propose a proximal point algorithm for finding the approximate solutions of this class of variational inclusions the convergence criteria of the iterative sequences generated by our algorithm is discussed several special cases are also given

on an iterative method for variational inequalities a number of numerical solutions are presented as examples of a new iterative method for variational inequalities the iterative method is based on the reduction of variational inequalities to the wiener hopf equations for obstacle problems the convergence is guaranteed inw 1 p spaces forp 2 the examples presented are one and two dimensional obstacle problems in cases when the greens function is known but the method is very general

rigidity of holomorphic mappings and a new schwarz lemma at the boundary a rigidity theorem for holomorphic mappings in the nature of the uniqueness statement of the classical one variable schwarz lemma is proved at the boundary of a strongly pseudoconvex domain the result reduces to an interesting and apparently new result even in one complex dimension the theorem has a variety of geometric and analytic interpretations department of mathematics university of michigan ann arbor michigan 48109 department of mathematics box 1146 washington university in st louis st louis missouri 63130 this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 04 utc all use subject to http about jstor org terms

domains with non compact automorphism group a survey abstract we survey results arising from the study of domains in c n with non compact automorphism group beginning with a well known characterization of the unit ball we develop ideas toward a consideration of weakly pseudoconvex and even non pseudoconvex domains with particular emphasis on characterizations of i smoothly bounded domains with non compact automorphism group and ii the levi geometry of boundary orbit accumulation points particular attention will be paid to results derived in the past ten years

iterative methods for linear complementarity problems with upperbounds on primary variables this paper is concerned with iterative methods for the linear complementarity problem lcp of findingx and y in rn such thatc dx y 0 b x 0 andxt c dx y yt b x 0 whenb 0 this is the lcp m q withm l 0d t which is in turn equivalent to a linear variational inequality over a rectangle this type of problem arises for example from quadratic programming qp problems with upper and lower bounds ifd is symmetric and from multicommodity market equilibrium problems with institutional price controls imposed ifd is not necessarily symmetric iterative methods for the lcp m q with symmetricm are well developed and studied using qp applications for nonsymmetric cases withm being either an h matrix with positive diagonals or a z matrix there exists a robust iterative method with guaranteed convergence this paper extends this algorithm so that the lcp m q withm l 0d t which is neither symmetric nor an h matrix with positive diagonals nor a z matrix can be processed when onlyd notm satisfies such properties the case whered is nonsymmetric is explicitly discussed

perturbed proximal point algorithms for generalized quasivariational inclusions abstract in this paper we study a class of generalized quasivariational inclusions by using the properties of the resolvent operator associated with a maximal monotone mapping in hilbert space we have established an existence theorem of solutions for generalized quasivariational inclusions suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions as special cases some known results in this field are also discussed

families of riemann surfaces uniformization and arithmeticity first published in transactions of the american mathematical society 370 2018 published by american mathematical society

solving third order obstacle problems with quartic b splines in this paper we develop a new numerical method for solving a system of third order boundary value problems associated with third order obstacle problems using the quartic b splines the convergence order of the method is considered and numerical results are also given

goldilocks domains a weak notion of visibility and applications in this paper we introduce a new class of domains in complex euclidean space called goldilocks domains and study their complex geometry these domains are defined in terms of a lower bound on how fast the kobayashi metric grows and an upper bound on how fast the kobayashi distance grows as one approaches the boundary strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this goldilocks condition but we also present families of goldilocks domains that have low boundary regularity or have boundary points of infinite type we will show that the kobayashi metric on these domains behaves in some sense like a negatively curved riemannian metric in particular it satisfies a visibility condition in the sense of eberlein and o neill this behavior allows us to prove a variety of results concerning boundary extension of maps and to establish wolff denjoy theorems for a wide collection of domains c 2017 elsevier inc all rights reserved

algorithm of solutions for mixed implicit quasi variational inequalities with fuzzy mappings abstract in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of mixed implicit quasi variational inequalities with fuzzy mappings are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given as special cases of these results the open problem put forward by noor is answered positively our results are new and generalize a number of known results to mixed implicity quasi variational inequalities with fuzzy mappings

a new class of completely generalized quasi variational inclusions in banach spaces in this paper a new notion of j proximal mapping for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space is introduced the existence and lipschitz continuity of j proximal mapping of a lower semicontinuous subdifferentiable proper functional are proved by applying the concept we introduce and study a new class of completely generalized quasi variational inclusions in reflexive banach spaces a novel and innovative iterative algorithm for finding the approximate solutions is suggested and analyzed the convergence criteria of the iterative sequences generated by the new iterative algorithm is also given these algorithm and existence result generalize many known results under hilbert space setting in recent literature to reflexive banach spaces

some techniques for solving absolute value equations in this paper we introduce and analyze two new methods for solving the np hard absolute value equations ave a x x b where a is an arbitrary n n real matrix and b rn in the case singular value of a exceeds 1 the comparison with other known methods is carried to show the effectiveness of the proposed methods for a variety of randomly generated problems the ideas and techniques of this paper may stimulate further research

iterative methods for a class of complementarity problems abstract in this paper we propose and study an algorithm for a new class of complementarity problems of finding u r n such that u 0 tu a u 0 u tu a u 0 where t is a continuous mapping and a is a nonlinear transformation from r n into itself it is proved that the approximate solution obtained from the iterative scheme converges to the exact solution several special cases are also discussed

a characterization of domains in c 2 with noncompact automorphism group let d be a bounded domain in c 2 with a non compact group of holomorphic automorphisms model domains for d are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth real analytic and of finite type

iterative algorithm for finding approximate solutions of mixed quasi variational like inclusions in the present paper we introduce the concept of h relaxed strong convexity of a differentiable functional and extend ding and yao s auxiliary variational inequality technique x p ding j c yao existence and algorithm of solutions for mixed quasi variational like inclusions in banach spaces computers and mathematics with applications 49 2005 857 869 to develop iterative algorithms for finding the approximate solutions to the mixed quasi variational like inclusion problem in short mqvlip in a banach space on the one hand we establish a result on the existence of a solution to the equilibrium problem by virtue of well known brouwer s fixed point theorem moreover by using this result we derive the existence and uniqueness of a solution to the mqvlip and the existence of the approximate solutions generated by the algorithm for the mqvlip on the other hand we use the concepts of h relaxed strong convexity of a differentiable functional and h cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the mqvlip

characterization of the bidisc by its automorphism group by a convex domain we mean an open set which contains the line segment joining any two points of it in the above statement g lim 0 gj relative to the compact open topology is a holomorphic mapping from d to 02 clearly the image g d must lie on ad i e the boundary of d condition 1 simply means that g d is a complex one dimensional subvariety in 02 one has to pay attention that we haven t assumed the whole boundary to be cl regularity of the boundary has only been assumed for an open subset u on ad which contains g d in fact under the assumptions of our theorem the boundary could never be globally smooth because this would imply the contradiction that a2 is biholomorphic to the euclidean ball by the argument in 10 the converse of our theorem is obviously true i e a2 satisfies all conditions 1 2 3 our result can be compared with the theorem due to s frankel 3 which asserts that a convex bounded domain covering a compact complex manifold

the automorphism group and limit set of a bounded domain i the finite type case abstract for bounded pseudoconvex domains with finite type we give a precise description of the automorphism group if an orbit of the automorphism group accumulates on at least two different points of the boundary then the automorphism group has finitely many components and is the almost direct product of a compact group and connected lie group locally isomorphic to aut b k further the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2 k 1 as applications we prove a new finite jet determination theorem and a tits alternative theorem the geometry of the kobayashi metric plays an important role in the paper

existence and algorithm of solutions for mixed quasi variational like inclusions in banach spaces in this paper we study a class of mixed quasi variational like inclusion with a bifunction in reflexive banach spaces by applying a minimax inequality due to the first author some existence and uniqueness theorems of solutions for the mixed quasi variational like inclusions are proved next by applying the auxiliary variational inequality technique we suggest an iterative algorithm to compute the approximate solutions of the mixed quasi variational like inclusions the convergence criteria of the algorithm is studied under quite mild conditions our results represent improvement and generalization of the previously known results in literature

existence and algorithm of solutions for generalized strongly nonlinear mixed variational like inequalities in banach spaces in this paper we introduce and study a class of generalized strongly nonlinear mixed variational like inequalities in reflexive banach spaces the auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for generalized strongly nonlinear mixed variational like inequalities first the existence of solutions of the auxiliary problems for the generalized strongly nonlinear mixed variational like inequalities is shown second an iterative algorithm for solving the generalized strongly nonlinear mixed variational like inequalities is constructed by using this existence result finally not only the existence of solutions of the generalized strongly nonlinear mixed variational like inequalities is shown but also the convergence of iterative sequences generated by the algorithm is also proven

on a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth on etudie le comportement asymptotique de varietes de riemann on construit des coordonnees a l infini sous certaines conditions intrinseques

merit functions for general variational inequalities in this paper we consider some classes of merit functions for general variational inequalities using these functions we obtain error bounds for the solution of general variational inequalities under some mild conditions since the general variational inequalities include variational inequalities quasivariational inequalities and complementarity problems as special cases results proved in this paper hold for these problems in this respect results obtained in this paper represent a refinement of previously known results for classical variational inequalities

splitting methods for pseudomonotone mixed variational inequalities we consider and analyze some new splitting methods for solving monotone mixed variational inequalities by using the technique of updating the solution the modified methods converge for monotone and pseudomonotone continuous operators the new splitting methods differ from the existing splitting methods the new results are versatile and proof of convergence is very simple

an iterative algorithm for variational inequalities abstract in this paper we introduce and study a new class of nonlinear variational inequalities this new class enables us to apply variational techniques to the solution of differential equations of both odd and even orders a projection method is used to suggest an iterative algorithm for finding the approximate solution of this class we also discuss the convergence criteria of the proposed iterative algorithm several special cases are discussed which can be obtained from the general result

a thermodynamical formalism for monge ampere equations moser trudinger inequalities and kahler einstein metrics we develop a variational calculus for a certain free energy functional on the space of all probability measures on a kahler manifold x this functional can be seen as a generalization of mabuchi s k energy functional and its twisted versions to more singular situations applications to monge ampere equations of mean field type twisted kahler einstein metrics and moser trudinger type inequalities on miller manifolds are given tian s alpha invariant is generalized to singular measures allowing in particular a proof of the existence of kahler einstein metrics with positive ricci curvature that are singular along a given anti canonical divisor which combined with very recent developments concerning miller metrics with conical singularities confirms a recent conjecture of donaldson as another application we show that if the calabi flow in the anti canonical class exists for all times then it converges to a kahler einstein metric when a unique one exists which is in line with a well known conjecture c 2013 elsevier inc all rights reserved

blowing up and desingularizing constant scalar curvature kahler manifolds this paper is concerned with the existence of constant scalar curvature kahler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature kahler metrics we also consider the desingularization of isolated quotient singularities of compact orbifolds which carry constant scalar curvature kahler metrics

stationary holomorphic discs and finite jet determination problems we construct a family of small analytic discs attached to levi non degenerate hypersurfaces in mathbb c n 1 which is globally biholomorphically invariant we then apply this technique to study unique determination problems along levi non degenerate hypersurfaces that are merely of class mathcal c 4 this method gives 2 jet determination results for germs of biholomorphisms cr diffeomorphisms as well as in the almost complex setting

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

sensitivity analysis in variational inequalities in this paper we derive conditions for the local uniqueness continuity and differentiability of a solution of parametric variational inequalities our approach is new and has a strong geometric flavor as an illustration we discuss the sensitivity of the classical complementarity problem

compactification of complete kahler manifolds of negative ricci curvature soit m une variete de kahler complete de dimension m et soit la forme de kahler on suppose 1 ric 0 2 m est tres fortement m 2 pseudoconcave 3 le recouvrement universel de m est de stein alors m est biholomorphe a une variete quasiprojective

on the proper holomorphic equivalence for a class of pseudoconvex domains a complete and explicit description of the holomorphic proper mappings between weakly pseudoconvex domains of the class ap see below is given the study of proper holomorphic mappings i e holomorphic mappings which antitransform compact sets into compact sets 1 f d d2 d1 d2 c cn n 1 between bounded pseudoconvex domains with smooth boundary has had recently a considerable impulse and has been applied mainly to investigate a under which hypothesis there is no obstruction for the existence of such an f b the regularity up to the boundary of 1 c for which domains proper means in effect biholomorphic the first class of problems has been taken into consideration for instance in 8 5 4 and a typical result is for example that a strictly pseudoconvex domain cannot be mapped properly onto a weakly pseudoconvex domain about b see for instance 4 2 3 and the bibliography there included the property enunciated in c has been proved in the case d d2 unit ball see 1 and 9 when d and d2 are strictly pseudoconvex domains with in addition d2 simply connected see 7 and 4 and in the case d d2 and strictly pseudoconvex see 7 the aim of this note is to look at questions of type a and c above posed for the following class of weakly pseudoconvex domains ap z 1j z2p lzn 2pn p pn e z n precisely we prove theorem in order for a proper holomorphic mapping from ap onto a q to exist it is necessary and sufficient that plq p llql pnlqn e z furthermore assuming the only proper holomorphic mapping between a p and a q is up to biholomorphisms of a q f z zfl l zpnqn received by the editors october 25 1982 and in revised form march 29 1983 1980 mathematics subject classification primary 32h99 secondary 32f15 work performed with finanical aid from m p i di1984 american mathematical society 0002 9947 84 1 00 25 per page

quaternion structure on the moduli space of yang mills connections soit m h un 2 tore complexe avec une metrique plate ou une surface k3 a metrique de ricciplate soit p un fibre g principal sur m g est un groupe de lie compact simple et l espace des modules des connexions irreductibles anti auto duales sur p alors la variete de rieman admet une structure de quaternion constante de facon covariante son groupe d holonomie est contenu dans sp n 4n dim r

on kahler einstein metrics on certain kahler manifolds with c1 m 0 on demontre qu il existe une metrique de kahler einstein sur une hypersurface de fermat a m dimensions de degre superieur a m 1

completely generalized multivalued nonlinear co quasi variational like inclusions in this paper we introduce and study completely generalized multivalued nonlinear co quasi variational like inclusions by using j h proximal mapping 1 we propose an iterative algorithm for computing the approximate solutions of completely generalized multivalued nonlinear co quasi variational like inclusions problem we prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized multivalued nonlinear co quasi variational like inclusions problem some special cases are also discussed

convergence of calabi yau manifolds abstract in this paper we study the convergence of calabi yau manifolds under kahler degeneration to orbifold singularities and complex degeneration to canonical singularities including the conifold singularities and the collapsing of a family of calabi yau manifolds

kahler einstein metrics with edge singularities this article considers the existence and regularity of kahler einstein metrics on a compact kahler manifold m with edge singularities with cone angle 2 along a smooth divisor d we prove existence of such metrics with negative zero and some positive cases for all cone angles 2 2 the results in the positive case parallel those in the smooth case we also establish that solutions of this problem are polyhomogeneous i e have a complete asymptotic expansion with smooth coecients along d for all 2 2

smooth hypersurfaces with a cr contraction abstract in this paper we show that a c real hypersurface in c n 1 of finite d angelo type admitting a weakly contracting local cr automorphism is cr equivalent to a weighted homogeneous hypersurface as an application we show that a bounded pseudoconvex domain in c n 1 with c boundary of finite d angelo type with a hyperbolic orbit accumulation point is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial

existence and iterative approximations of solutions for mixed quasi variational like inequalities in banach spaces abstract in this paper we introduce and investigate a new class of mixed quasi variational like inequalities in reflexive banach spaces by applying a minimax inequality due to ding tan and a lemma due to chang we establish some existence and uniqueness results of solution for the mixed quasi variational like inequality next by using a kkm theorem due to fan and an auxiliary principle technique due to cohen we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms our results extend improve and unify several known results in the literature

some discretizations of geometric evolution equations and the ricci iteration on the space of kahler metrics we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamics on certain infinite dimensional spaces we illustrate the fruitfulness of this approach in the context of the ricci flow as well as another flow in kahler geometry we introduce and study dynamical systems related to the ricci operator on the space of kahler metrics that arise as discretizations of these flows we pose some problems regarding their dynamics we point out a number of applications to well studied objects in kahler and conformal geometry such as constant scalar curvature metrics kahler ricci solitons nadel type multiplier ideal sheaves balanced metrics the moser trudinger onofri inequality energy functionals and the geometry and structure of the space of kahler metrics e g we obtain a new sharp inequality strengthening the classical moser trudinger onofri inequality on the two sphere

quasi variational inequalities and applications to the traffic equilibrium problem discussion of a paradox abstract this paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of a quasi variational inequality it is shown that the solving procedure proposed by maugeri 1987 with respect to the fixed demands model is also available when the equilibrium problem with elastic demands is expressed in terms of a quasi variational inequality a numerical example is presented to illustrate the computational procedure and to discuss a paradox moreover a theorem that ensures the existence of a solution of the quasi variational inequality is exhibited

general nonlinear variational inequalities abstract the fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities several special cases which can be obtained from our main result are also discussed

algorithm for solving a new class of general mixed variational inequalities in banach spaces in this paper a new concept of h proximal mapping for a proper subdifferentiable functional which may not be convex on a banach space is introduced an existence and lipschitz continuity of the h proximal mapping are proved by using properties of the h proximal mapping a new class of general mixed variational inequalities is introduced and studied in banach spaces an existence theorem of solutions is established and a new iterative algorithm for solving the general mixed variational inequality is suggested a convergence criteria of the iterative sequence generated by the new algorithm is also given

exchange price equilibria and variational inequalities the aim of this paper is to show the relevance of the concept and the theory of variational inequalities in the study of economic equilibria

sensitivity analysis framework for variational inequalities in this paper a sensitivity analysis framework is developed for variational inequalities the perturbed solution to a parametric variational inequality problem is shown to be continuous and directionally differentiable under appropriate second order and regularity assumptions moreover this solution is once continuously differentiable if strict complementarity also holds

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

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

some resolvent iterative methods for variational inclusions and nonexpansive mappings in this paper we suggest and analyze three step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique we also study the convergence criteria of three step iterative method under some mild conditions our results include the previous results of noor m aslam noor general variational inequalities and nonexpansive mappings j math anal appl 331 2007 810 822 and noor and huang m aslam noor zhenyu huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press doi 10 1016 j amc 2006 08 088 as special cases and may be considered as an improvement and refinement of the previously known results

existence and algorithm of solutions for nonlinear mixed variational like inequalities in banach spaces in this paper we study a new class of nonlinear mixed variational like inequalities in reflexive banach spaces by applying a minimax inequality due to author we first prove an existence uniqueness theorem of solutions for the nonlinear mixed variational like inequalities next we extend the auxiliary problem technique under reflexive banach space setting to suggest and analyze an innovative iterative algorithm to compute the approximate solutions of the nonlinear mixed variational like inequalities the convergence criteria of the iterative algorithm is also given these results improve and generalize many known results in recent literature

the existence of kahler einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group on utilise la methode de continuite pour demontrer l existence de metriques de kahler einstein pour des varietes de kahler de fibre linge positif anticanonique sous l hypothese additionnelle de l existence d un bon groupe de symetries fini ou compact

some new projection methods for variational inequalities in this paper we propose some new double projection methods for solving variational inequalities by using the wiener hopf equations technique it is shown that these methods converge linearly under mild conditions and include some existing projection methods as special cases some examples are given to illustrate the efficiency of the proposed methods

strong convergence of three step relaxed hybrid steepest descent methods for variational inequalities in this paper we prove the strong convergence of a three step relaxed hybrid steepest descent method for solving variational inequalities under some suitable conditions our result can be considered as an improvement and refinement of the previously known results

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

on general hemiequilibrium problems in this paper we introduce and analyze a new class of equilibrium problems known as general hemiequilibrium problems it is shown that this class includes hemiequilibrium problems hemivariational inequalities and complementarity problems as special cases we use the auxiliary principle techniques to suggest some iterative type methods for solving multivalued hemiequilibrium problems we also analyze the convergence analysis of these new iterative methods under some mild conditions as special cases we obtain several new and known methods for solving variational inequalities and equilibrium problems

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

parametrization of local cr automorphisms by finite jets and applications the goal of this work is to study the structure of the group of all local realanalytic cr automorphisms of a germ of a real analytic hypersurface m p in c or equivalently of all local biholomorphisms h c p c p mapping the germ m p into itself we also deal with the more general situation of a realanalytic cr manifold of arbitrary codimension see 2 for every fixed point p m we refer to this group of local biholomorphisms as the stability group of m p and denote it by aut m p endowed with the topology of uniform convergence on compact neighbourhoods of p it becomes a topological group this natural inductive limit topology can be described in the following way a sequence of germs of biholomorphisms hj aut m p converges to another such germ h aut m p if there exists a neighbourhood u of p in c to which all mappings hj extend holomorphically and such that hj h uniformly on u this group arises in a variety of different circumstances one of the most important ones where it naturally appears is the biholomorphic equivalence problem which consists in deciding whether two given germs of real analytic hypersurfaces are biholomorphically equivalent the biholomorphic equivalence problem has been studied since the beginning of the last century when poincare 37 observed probably for the first time that two real hypersurfaces in c for n 2 are not necessarily locally equivalent via a holomorphic transformation though they are via a c transformation today the biholomorphic equivalence problem for strongly pseudoconvex or levi nondegenerate hypersurfaces is pretty well understood based on the works of e cartan 14 15 in dimension two and the results of tanaka 42 and chern moser 17 in arbitrary dimension thanks to the works initiated in the 1970s a number of remarkable properties of the stability group of strongly pseudoconvex real analytic hypersurfaces have been discovered see e g the surveys by vitushkin 45 huang 30 and baouendi ebenfelt and rothschild 5 for complete discussions on this matter these properties depend on whether the germ m p can be biholomorphically mapped onto a piece of the unit sphere if there exists such a biholomorphism one says that m p is spherical for instance if m p is not spherical the group aut m p is

general iterative algorithms for solving mixed quasi variational like inclusions in this paper we extend the auxiliary variational inequality technique due to ding and yao x p ding j c yao existence and algorithm of solutions for mixed quasi variational like inclusions in banach spaces comput math appl 49 2005 857 869 to develop iterative algorithms for finding the approximate solutions of a mixed quasi variational like inclusion problem in short mqvlip in the setting of banach spaces we first establish a result on the existence of a solution of the equilibrium problem by virtue of the fan kkm lemma then by using this result and a result by ding and tan x p ding k k tan a minimax inequality with applications to existence of equilibrium point and fixed point theorems colloq math 63 2 1992 233 247 we derive the existence of a unique solution of mqvlip and the existence of approximate solutions generated by the proposed algorithms moreover we also provide the new criteria for convergence of approximate solutions to the exact solution of mqvlip

on a class of variational inequalities in this paper we introduce and study a new unified and general class of variational inequalities we derive the general error estimates for the finite element solutions of variational inequalities it has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities several special cases which can be obtained from the general results are also discussed

kahler einstein metrics on complex surfaces with c 1 0 various estimates of the lower bound of the holomorphic invariant m defined in t are given here by using branched coverings potential estimates and lelong numbers of positive d closed 1 1 currents of certain type etc these estimates are then applied to produce kahler einstein metrics on complex surfaces withc1 0 in particular we prove that there are kahler einstein structures withc1 0 on any manifold of differential type cp 2 overline ncp 2 3 leqq n leqq 8

general algorithm of solutions for nonlinear variational inequalities in banach space abstract in this paper we shall study a class of general nonlinear variational inequalities in reflexive banach spaces by applying a minimax inequality obtained by the author some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved next by applying the auxiliary problem technique we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality finally the convergence criteria is also discussed

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

a class of projection methods for general variational inequalities abstract in this paper we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the wiener hopf equations technique the modified methods converge for pseudomonotone operators our proof of convergence is very simple as compared with other methods the proposed methods include several known methods as special cases

letter to the editor on a unified implicit method for variational inequalities it is well known that variational inequalities are equivalent to fixed point problems we use this equivalent formulation to suggest and analyze a new unified implicit method of solving variational inequalities this new method includes several known implicit and extragradient methods as special cases we prove that the convergence of this new method requires only the pseudomonotonicity of the operator which is a weaker condition than monotonicity several special cases are discussed an example is given to illustrate the implementation of the proposed method a comparison with other methods shows that the present method performs better

convergence and finite determination of formal cr mappings in this paper we study the convergence and finite determination of formal holomorphic mappings of c 0 taking one real submanifold into another by a formal holomorphic mapping h c 0 c 0 we mean an n vector h h1 hn where each hj is a formal power series in n indeterminates with no constant term if m and m are real smooth submanifolds through 0 in c defined near the origin by z z 0 and z z 0 respectively where and are vector valued smooth defining functions then we say that a formal mapping h c 0 c 0 sends m into m if the vector valued power series h z h z is a matrix multiple of z z for real analytic hypersurfaces we shall prove the following theorem 1 let m and m be real analytic hypersurfaces through the origin in c n 2 assume that neither m nor m contains a nontrivial holomorphic subvariety through 0 then any formal mapping h c 0 c 0 sending m into m is convergent the condition that m above does not contain a nontrivial holomorphic subvariety is necessary see remark 2 3 as a corollary we obtain the following characterization

finite jet determination of cr mappings abstract we prove the following finite jet determination result for cr mappings given a smooth generic submanifold m c n n 2 that is essentially finite and of finite type at each of its points for every point p m there exists an integer l p depending upper semicontinuously on p such that for every smooth generic submanifold m c n of the same dimension as m if h 1 h 2 m p m are two germs of smooth finite cr mappings with the same l p jet at p then necessarily j p k h 1 j p k h 2 for all positive integers k in the hypersurface case this result provides several new unique jet determination properties for holomorphic mappings at the boundary in the real analytic case in particular it provides the finite jet determination of arbitrary real analytic cr mappings between real analytic hypersurfaces in c n of d angelo finite type it also yields a new boundary version of h cartan s uniqueness theorem if c n are two bounded domains with smooth real analytic boundary then there exists an integer k depending only on the boundary such that if h 1 h 2 are two proper holomorphic mappings extending smoothly up to near some point p and agreeing up to order k at p then necessarily h 1 h 2

existence and algorithm of solutions for generalized mixed implicit quasi variational inequalities1this project was supported by the national science foundation of people s republic china 1 in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of generalized mixed implicit quasi variational inequalities are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria are also given as special cases of these results the open problem put forward by noor is answered positively and some results of existence and algorithm of solutions for generalized implicit quasi complementarity problems are also obtained our results are new and generalize a number of known results of mixed variational inequalities mixed quasi variational inequalities and quasi complementary problems involving single valued and set valued mappings in recent literatures

determination of formal cr mappings by a finite jet abstract we prove that if m is a connected real analytic holomorphically nondegenerate hypersurface in c n 1 then for any point p m there exists an integer k such that any two germs at p of local biholomorphic mappings h 1 h 2 c n 1 p c n 1 p that send m into itself and whose k jets agree at p are identical the above is a special case of a more general theorem stated for formal hypersurfaces that gives a finite jet determination result for the class of formal mappings whose jacobian determinant does not vanish identically