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

iterative approaches to convex feasibility problems in banach spaces abstract the convex feasibility problem cfp of finding a point in the nonempty intersection i 1 n c i is considered where n 1 is an integer and each c i is assumed to be the fixed point set of a nonexpansive mapping t i x x with x a banach space it is shown that the iterative scheme x n 1 n 1 y 1 n 1 t n 1 x n is strongly convergent to a solution of cfp provided the banach space x either is uniformly smooth or is reflexive and has a weakly continuous duality map and provided the sequence n satisfies certain conditions the limit of x n is located as q y where q is the sunny nonexpansive retraction from x onto the common fixed point set of the t i s

deformation of canonical morphisms and the moduli of surfaces of general type in this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space among other things we prove a criterion that determines when a finite map can be deformed to a one to one map we use this criterion to construct new surfaces of general type with birational canonical map for different c 1 2 and the canonical map of the surfaces we construct is in fact a finite birational morphism our general results enable us to describe some new components of the moduli of surfaces of general type we also find infinitely many moduli spaces open image in new window having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism

the plus closure of an ideal abstract if r is a local integral domain let r denote the integral closure of r in an algebraic closure of its quotient field if z r we would like to understand the conditions under which z ir where i is an ideal of r necessary and sufficient conditions on the coefficients of the minimal irreducible polynomial for z are known when i is generated by two elements of a regular system of parameters and when z is in a degree two extension of r in this article we obtain results for the case when z 3 r as well as a sufficient condition for z to be in ir when z a r for a 1 and i has a finite number of generators

implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings in this paper we propose a new implicit iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings we establish some convergence theorems for this implicit iteration scheme in particular necessary and sufficient conditions for strong convergence of this implicit iteration scheme were obtained

hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings abstract recently takahashi and takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 2006 doi 10 1016 j jmaa 2006 08 036 suggested and analyzed 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 in this paper we introduce a new 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 common fixed points of infinitely many nonexpansive mappings in a hilbert space then we prove a strong convergence theorem which is the improvements and extension of takahashi and takahashi s 2006 corresponding result using this theorem we obtain two corollaries which improve and extend their corresponding results

extended plus closure and colon capturing abstract three results concerning the colon capturing property for extended plus closures in excellent mixed characteristic rings are demonstrated it is shown that the extended plus closure has the colon capturing property for arbitrary sets of three parameters it is also seen that establishing the colon capturing property for the extended plus closure is sufficient to guarantee the existence of balanced big cohen macaulay algebras also for three dimensional complete domains the second local cohomology of r is annihilated by arbitrarily small powers of every non unit

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

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0