sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems in this paper a new iterative scheme by hybrid method is constructed strong convergence of the scheme to a common element of the set of common fixed points of finite family of relatively quasi nonexpansive mappings and set of common solutions of a system of equilibrium problems in a uniformly convex and uniformly smooth real banach space is proved using the properties of generalized f projection operator our results extend important recent results

a variational analysis of the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface we will give existence results by using variational methods in a noncoercive case a key tool in our analysis is a new moser trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u1 and u2 2012 wiley periodicals inc

a hybrid iterative scheme for mixed equilibrium problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem mep and the set of common fixed points of finitely many nonexpansive mappings in a real hilbert space first by using the well known kkm technique we derive the existence and uniqueness of solutions of the auxiliary problems for the mep second by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings furthermore we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings

maximal solution of the liouville equation in doubly connected domains abstract in this paper we consider the liouville equation u 2 e u 0 with dirichlet boundary conditions in a two dimensional doubly connected domain we show that there exists a simple closed curve such that for a sequence n 0 and a sequence of solutions u n it holds u n log 1 n h where h is a harmonic function in and n 2 log 1 n e u n d x 8 c where c is a constant depending on the conformal class of only

a singular sphere covering inequality uniqueness and symmetry of solutions to singular liouville type equations we derive a singular version of the sphere covering inequality which was recently introduced in gui and moradifam invent math https doi org 10 1007 s00222 018 0820 2 2018 suitable for treating singular liouville type problems with superharmonic weights as an application we deduce new uniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains as well as new self contained proofs of previously known results such as the uniqueness of spherical convex polytopes first established in luo and tian proc am math soc 116 4 1119 1129 1992 furthermore we derive new symmetry results for the spherical onsager vortex equation

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

two extragradient methods for generalized mixed equilibrium problems nonexpansive mappings and monotone mappings in this paper we introduce iterative schemes based on the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of an infinite a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we obtain some weak convergence theorems for the sequences generated by these processes in hilbert spaces the results in this paper generalize extend and unify some well known weak convergence theorems in the literature

on the invariant measures for the two dimensional euler flow it is proven that the canonical gibbs measure associated with a gas of vortices of intensity converges in the limitn 0 n const to a gaussian measure which is invariant for the two dimensional euler equation

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

singular mean field equations on compact riemann surfaces for a general class of elliptic pde s in mean field form on compact riemann surfaces with exponential nonlinearity we address the question of the existence of solutions with concentrated nonlinear term which in view of the applications are physically of definite interest in the model we also include the possible presence of singular sources in the form of dirac masses which makes the problem more difficult to attack

existence and multiplicity result for the singular toda system abstract we consider the toda system on a compact surface g u 1 2 1 h 1 e u 1 h 1 e u 1 d v g 1 2 h 2 e u 2 h 2 e u 2 d v g 1 4 j 1 j 1 j p j 1 u 2 2 2 h 2 e u 2 h 2 e u 2 d v g 1 1 h 1 e u 1 h 1 e u 1 d v g 1 4 j 1 j 2 j p j 1 where h i are smooth positive functions i are positive real parameters p j are given points on and i j are numbers greater than 1 we give existence and multiplicity results using variational and morse theoretical methods it is the first existence result when some of the i j s are allowed to be negative

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

convergence theorems for equilibrium problems and fixed point problems of a finite family of asymptotically k strictly pseudocontractive mappings in the intermediate sense in this paper we introduce a modified explicit iterative process for finding a common element of the solutions of an equilibrium problem and the set of common fixed points of a finite family of asymptotically k strictly pseudocontractive mappings in the intermediate sense in the framework of hilbert spaces we get a weak convergence theorem for finding a common element of the above two sets and then we modify these algorithms to have a strong convergence theorem by using a hybrid method in the mathematical programming our results improve and extend the recent ones announced by many others

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

compactness of solutions to some geometric fourth order equations we prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds the proof is based on a refined bubbling analysis for which the main estimates are given in integral form our result is used in a subsequent paper to find critical points via minimax arguments of some geometric functional which give rise to conformal metrics of constant q curvature as a byproduct of our method we also obtain compactness of such metrics

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

a system of mixed equilibrium problems fixed point problems of strictly pseudo contractive mappings and nonexpansive semi groups the purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems the set of common fixed points for an infinite family of strictly pseudo contractive mappings and the set of common fixed points for nonexpansive semi groups in hilbert space under suitable conditions some strong convergence theorem are proved the results presented in the paper extend and improve some recent results

hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi ϕ nonexpansive mappings in banach spaces abstract in this paper we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex banach space which has the kadec klee property the results presented in the paper improve and extend some recent results

non degeneracy and uniqueness of solutions to singular mean field equations on bounded domains abstract the aim of this paper is to complete the program initiated in 51 23 and then carried out by several authors concerning non degeneracy and uniqueness of solutions to mean field equations in particular we consider mean field equations with general singular data on non smooth domains the argument is based on the alexandrov bol inequality and on the eigenvalues analysis of linearized singular liouville type problems

strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications the purpose of this paper is by using the hybrid iterative method to prove some strong convergence theorems for approximating a common element of the set of solutions to a system of generalized mixed equilibrium problems and the set of common fixed points for two countable families of closed and asymptotically relatively nonexpansive mappings in banach space the results presented in the paper improve and extend the corresponding results of su et al y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3906 li and su h y li y f su strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems nonlinear anal 72 2 2010 847 855 chang et al s s chang h w joseph lee chi kin chan a new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in banach spaces with applications nonlinear anal tma 73 2010 2260 2270 kang et al j kang y su x zhang hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications nonlinear anal hs 4 4 2010 755 765 matsushita and takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 tan et al j f tan s s chang m liu j i liu strong convergence theorems of a hybrid projection algorithm for a family of quasi asymptotically nonexpansive mappings opuscula math 30 3 2010 341 348 takahashia and zembayashi w takahashi k zembayashi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 and wattanawitoon and kumam k wattanawitoon p kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid systems 3 2009 11 20 and others

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

optimal calibration for multiple testing against local inhomogeneity in higher dimension based on two independent samples x 1 x m and x m 1 x n drawn from multivariate distributions with unknown lebesgue densities p and q respectively we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q the construction is built from randomized nearest neighbor statistics it does not require any preliminary information about the multivariate densities such as compact support strict positivity or smoothness and shape properties the properly adjusted multiple testing procedure is shown to be sharp optimal for typical arrangements of the observation values which appear with probability close to one the proof relies on a new coupling bernstein type exponential inequality reflecting the non subgaussian tail behavior of a combinatorial process for power investigation of the proposed method a reparametrized minimax set up is introduced reducing the composite hypothesis p q to a simple one with the multivariate mixed density m n p 1 m n q as infinite dimensional nuisance parameter within this framework the test is shown to be spatially and sharply asymptotically adaptive with respect to uniform loss on isotropic holder classes the exact minimax risk asymptotics are obtained in terms of solutions of the optimal recovery

viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove a strong convergence theorem which is connected with combettes and hirstoaga s result p l combettes s a hirstoaga equilibrium programming in hilbert spaces j nonlinear convex anal 6 2005 117 136 and wittmann s result r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 using this result we obtain two corollaries which improve and extend their results

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

convergence theorems for equilibrium problem variational inequality problem and countably infinite relatively quasi nonexpansive mappings in this paper we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi nonexpansive mappings the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a inverse strongly monotone mapping in banach spaces our theorems improve generalize unify and extend several results recently announced

modified block iterative algorithm for quasi ϕ asymptotically nonexpansive mappings and equilibrium problem in banach spaces abstract the purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi asymptotically nonexpansive mappings and the set of an equilibrium problem under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex banach space with the kadec klee property as an application at the end of the paper a numerical example is given the results presented in the paper improve and extend the corresponding results in qin et al convergence theorems of common elements for equilibrium problems and fixed point problem in banach spaces j comput appl math 225 2009 20 30 zhou et al convergence theorems of a modified hybrid algorithm for a family of quasi asymptotically nonexpansive mappings j appl math compt 17 march 2009 doi 10 1007 s12190 009 0263 4 takahashi and zembayshi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 wattanawitoon and kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid syst 3 2009 11 20 and matsushita and takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 and others

generic multiplicity for a scalar field equation on compact surfaces we prove generic multiplicity of solutions for a scalar field equation on compact surfaces via morse inequalities in particular our result improves significantly the multiplicity estimate which can be deduced from the degree counting formula in chen and lin 2003 12 related results are derived for the prescribed q curvature equation

strong convergence of composite iterative methods for equilibrium problems and fixed point problems we introduce a new composite iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space it is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping our results substantially improve the corresponding results of takahashi and takahashi a takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 essentially a new approach for finding solutions of equilibrium problems and the fixed points of nonexpansive mappings is provided

supercritical mean field equations on convex domains and the onsager s statistical description of two dimensional turbulence we are motivated by the study of the microcanonical variational principle within onsager s description of two dimensional turbulence in the range of energies where the equivalence of statistical ensembles fails we obtain sufficient conditions for the existence and multiplicity of solutions for the corresponding mean field equation on convex and thin enough domains in the supercritical with respect to the moser trudinger inequality regime this is a brand new achievement since existence results in the supercritical region were previously known only on multiply connected domains we then study the structure of these solutions by the analysis of their linearized problems and we also obtain a new uniqueness result for solutions of the mean field equation on thin domains whose energy is uniformly bounded from above finally we evaluate the asymptotic expansion of those solutions with respect to the thinning parameter and combining it with all the results obtained so far we solve the microcanonical variational principle in a small range of supercritical energies where the entropy is shown to be concave

a new iterative method for equilibrium problems and fixed point problems of infinitely nonexpansive mappings and monotone mappings in this paper we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for a inverse strongly monotone mapping in hilbert spaces we prove that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main result improve and extend plubtieng and punpaeng s corresponding result s plubtieng r punpaeng a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings applied mathematics and computation 197 2008 548 558 using this theorem we obtain three corollaries

a hybrid extragradient method for approximating the common solutions of a variational inequality a system of variational inequalities a mixed equilibrium problem and a fixed point problem abstract in this paper we give a hybrid extragradient iterative method for finding the approximate element of the common set of solutions of a generalized equilibrium problem a system of variational inequality problems a variational inequality problem and a fixed point problem for a strictly pseudocontractive mapping in a real hilbert space further we establish a strong convergence theorem based on this method the results presented in this paper improves and generalizes the results given in yao et al 36 and ceng et al 7 and some known corresponding results in the literature

convergence theorems for mixed equilibrium problems variational inequality problem and uniformly quasi ϕ asymptotically nonexpansive mappings abstract we introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi asymptotically nonexpansive mappings the set of the variational inequality for an inverse strongly monotone operator the set of solutions of the mixed equilibrium problems then we obtain strong convergence theorems for the sequences generated by this process in a 2 uniformly convex and uniformly smooth banach space our results extend and improve ones from several earlier works

existence of conformal metrics with constant q curvature given a compact four dimensional manifold we prove existence of conformal metrics with constant q curvature under generic assumptions the problem amounts to solving a fourth order nonlinear elliptic equation with variational structure since the corresponding euler functional is in general unbounded from above and from below we employ topological methods and min max schemes jointly with the compactness result of 35

an iterative method for equilibrium problems and a finite family of relatively nonexpansive mappings in a banach space abstract in this paper we introduce a new iterative method for finding a common element of the set of fixed points of a finite family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly convex and uniformly smooth banach spaces then we prove a strong convergence theorem by using the generalized projection

approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense abstract in this paper we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly lipschitzian continuous and asymptotically i strict pseudocontractive mapping in the intermediate sense we prove the strong convergence theorem for a new iterative algorithm under some mild conditions in hilbert spaces finally we also give some numerical examples for support our results

strong convergence theorems for infinite family of relatively quasi nonexpansive mappings and systems of equilibrium problems abstract in this paper we construct a new iterative scheme by hybrid method for approximation of common element of set of common fixed points of countably infinite family of relatively quasi nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex and uniformly smooth real banach space using the properties of generalized f projection operator then we prove strong convergence of the scheme to a common element of the two sets furthermore we apply our results to solve convex minimization problem our results extend important recent results

negative temperature states and large scale long lived vortices in two dimensional turbulence we study onsager s theory of large coherent vortices in turbulent flows in the approximation of the point vortex model for two dimensional euler hydrodynamics in the limit of a large number of point vortices with the energy perpair of vortices held fixed we prove that the entropy defined from the microcanonical distribution as a function of the pair specific energy has its maximum at a finite value and thereafter decreases yielding the negative temperature states predicted by onsager we furthermore show that the equilibrium vorticity distribution maximizes an appropriate entropy functional subject to the constraint of fixed energy and under regularity assumptions obeys the joyce montgomery mean field equation we also prove that under appropriate conditions the vorticity distribution is the same as that for the canonical distribution a form of equivalence of ensembles we establish a large fluctuation theory for the microcanonical distributions which is based on a level 3 large deviations theory for exchangeable distributions we discuss some implications of that property for the ergodicity requirements to justify onsager s theory and also the theoretical foundations of a recent extension to continuous vorticity fields by r robert and j miller although the theory of two dimensional vortices is of primary interest our proofs actually apply to a very general class of mean field models with long range interactions in arbitrary dimensions

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

a hybrid iterative scheme for asymptotically k strict pseudo contractions in hilbert spaces abstract in this paper we introduce an explicit iterative process for a finite family of asymptotically k strict pseudo contractions by using the iterative process we get a weak convergence theorem for a finite family of asymptotically k strict pseudo contractions and then we modify these algorithms to have strong convergence in the framework of hilbert spaces our results improve and extend the recent ones announced by g l acedo h k xu iterative methods for strict pseudo contractions in hilbert spaces nonlinear anal 67 2007 2258 2271 t h kim h k xu strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 c martinez yanes h k xu strong convergence of the cq method for fixed point iteration processes nonlinear anal 64 2006 2400 2411 k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert space j math anal appl 329 2007 336 346 t h kim h k xu convergence of the modified manns iteration method for asymptotically strict pseudo contractions nonlinear anal 2007 doi 10 1016 j na 2007 02 029 and many others

weighted barycentric sets and singular liouville equations on compact surfaces given a closed surface we prove a general existence result for some elliptic pde with exponential nonlinearities and negative dirac deltas extending a theory recently obtained for the regular case this is done by global methods since the associated euler functional might be unbounded from below we define a new model space generalizing the so called space of formal barycenters and characterizing up to homotopy equivalence its low sublevels as a result the analytic problem is reduced to a topological one concerning the contractibility of this model space to this aim we prove a new functional inequality in the spirit of chen and li 1991 11 and then employ a min max scheme based on conical construction jointly with the blow up analysis in bartolucci and montefusco 2007 4 after bartolucci and tarantello 2002 brezis and merle 1991 and this study is motivated by abelian chern simons theory in self dual regime or from the problem of prescribing the gaussian curvature with conical singularities generalizing a problem raised in kazdan and warner 1974 24

strong convergence of a new composite iterative method for equilibrium problems and fixed point problems in this paper we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a hilbert space it is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings our results improve and extend the corresponding ones announced by many others

invariance principles for some farima and nonstationary linear processes in the domain of a stable distribution we prove some invariance principles for processes which generalize farima processes when the innovations are in the domain of attraction of a nongaussian stable distribution the limiting processes are extensions of the fractional levy processes the technique used is interesting in itself it extends an older idea of splitting a sample into a central part and an extreme one analyzing each part with different techniques and then combining the results this technique seems to have the potential to be useful in other problems in the domain of nongaussian stable distributions

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main theorem extends a recent result of yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings applied mathematics and computation 186 2 2007 1551 1558

the principal eigenvalue of a conformally invariant differential operator with an application to semilinear elliptic pde in this paper we give conditions under which the paneitz operator a conformally invariant fourth order differential operator is positive we also prove a sharp estimate for a related conformal invariant these results are combined to study the existence of a semilinear pde with critical sobolev growth

some considerations on the nonlinear stability of stationary planar euler flows we give sufficient conditions for the nonlinear stability of possibly nonsmooth stationary solutions of the two dimensional euler equation in symmetric bounded domains we use as lyapunov functions first integrals due to the symmetry of the problem moreover we investigate the stability of smooth solutions under perturbations of the boundary the last result is based on a generalization of the well known arnold approach

a double mean field equation related to a curvature prescription problem abstract we study a double mean field type pde related to a prescribed curvature problem on compacts surfaces with boundary 0 1 u 2 k e u k e u 1 in u 2 h e u 2 h e u 2 1 on here and are real parameters k h are smooth positive functions on and respectively and is the outward unit normal vector to we provide a general blow up analysis then a moser trudinger inequality which gives energy minimizing solutions for some range of parameters finally we provide existence of min max solutions for a wider range of parameters which is dense in the plane if is not simply connected

convergence theorems of shrinking projection methods for equilibrium problem variational inequality problem and a finite family of relatively quasi nonexpansive mappings we introduce a w mapping for a finite family of relatively quasi nonexpansive mappings and construct an iterative scheme for finding a common element of the solution set of equilibrium problem the solution set of the variational inequality problem for an inverse strongly monotone operator and set of common fixed points of a finite family of relatively quasi nonexpansive mappings strong convergence theorems are presented in a 2 uniformly convex and uniformly smooth banach space our results generalize and extend relative results

some results on generalized equilibrium problems involving a family of nonexpansive mappings abstract in this paper we introduce an iterative method for finding a common element in the solution set of generalized equilibrium problems in the solution set of variational inequalities and in the common fixed point set of a family of nonexpansive mappings strong convergence theorems are established in the framework of hilbert spaces

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

a high dimensional wilks phenomenon a theorem by wilks asserts that in smooth parametric density estimation the difference between the maximum likelihood and the likelihood of the sampling distribution converges toward a chi square distribution where the number of degrees of freedom coincides with the model dimension this observation is at the core of some goodness of fit testing procedures and of some classical model selection methods this paper describes a non asymptotic version of the wilks phenomenon in bounded contrast optimization procedures using concentration inequalities for general functions of independent random variables it proves that in bounded contrast minimization as for example in statistical learning theory the difference between the empirical risk of the minimizer of the true risk in the model and the minimum of the empirical risk the excess empirical risk satisfies a bernstein like inequality where the variance term reflects the dimension of the model and the scale term reflects the noise conditions from a mathematical statistics viewpoint the significance of this result comes from the recent observation that when using model selection via penalization the excess empirical risk represents a minimum penalty if non asymptotic guarantees concerning prediction error are to be provided from the perspective of empirical process theory this paper describes a concentration inequality for the supremum of a bounded non centered actually non positive empirical process combining the now classical analysis of m estimation building on talagrand s inequality for suprema of empirical processes and versatile moment inequalities for functions of independent random variables this paper develops a genuine bernstein like inequality that seems beyond the reach of traditional tools

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence