three step iterations for variational inequalities and nonexpansive mappings in this paper we introduce a new three step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution we show that the sequence converges strongly to a common element of two sets under some control conditions results proved in this paper may be viewed as an improvement and refinement of the recent results of noor and huang m aslam noor z huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press and yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput in press

on dynamic equations with deviating arguments abstract in this paper we study the existence of solutions of dynamic equations with deviating arguments on time scales we formulate sufficient conditions under which such problems have a minimal and a maximal solution in a corresponding region bounded by upper lower solutions

iteration processes for nonlinear mappings in convex metric spaces on considere le schema iteratif d ishikawa pour construire des points fixes d applications quasi contractives quasi contractives generalisees et quasi non dilatante dans des espaces metriques convexes

approximating the common fixed points of two sequences of uniformly quasi lipschitzian mappings in convex metric spaces in this paper a kind of ishikawa type iterative scheme with errors for approximating a common fixed point of two sequences of uniformly quasi lipschitzian mappings is introduced and studied in convex metric spaces under some suitable conditions the convergence theorems concerned with the ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi lipschitzian mappings were proved in convex metric spaces the results presented in the paper generalize and improve some recent results of wang and liu c wang l w liu convergence theorems for fixed points of uniformly quasi lipschitzian mappings in convex metric spaces nonlinear anal tma 70 2009 2067 2071

a new general iterative scheme for split variational inclusion and fixed point problems of k strict pseudo contraction mappings with convergence analysis in this paper we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of k strictly pseudo contractive nonself mappings strong convergence theorem is established under some suitable conditions in a real hilbert space which also solves some variational inequality problems results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors finally some examples to study the rate of convergence and some illustrative numerical examples are presented

arithmetic distance functions and height functions in diophantine geometry in virtually all areas of diophantine geometry the theory of height functions plays a crucial role this theory associates to each cartier divisor d on a projective variety v a function ho mapping the group of rational points of v to the real numbers this function which is defined up to a bounded function on v has very nice functorial properties for example it is linear in d and depends only on the linear equivalence class of d as a consequence any relation between divisor classes such as the theorem of the square for abelian varieties will yield a corresponding relation for height functions further it is possible to write the height function ho as a sum of local height functions 20 v where v ranges over the distinct absolute values of the given field these local heights are also known as logarithmic distance functions or weil functions each 2 o is defined away from the support of d and gives a measure of the v adic distance from the given point of v to the divisor d in this paper we propose to define local height functions 2 x for every closed subscheme x of a projective variety v as above 2x v will give a measure of the v adic distance from a point of v to x these functions will have many nice functorial properties for example 2xny will equal the minimum of 2x and hr in this way relations between closed subschemes or equivalently between ideal sheaves will yield relations between local height functions we will thus be able to convert geometric statements into arithmetic statements relatively painlessly more generally we will deal with the case that v is merely quasi projective by defining a function 20v v which will measure the v adic distance to the boundary of v we will then be able to assign to each closed subscheme x of v a local height function 2x which will be well defined up to addition of a multiple of 2 v this extra generality is useful for example when one has a complete family of varieties and wishes to discard the bad fibers as one application of the machinery that we have developed we prove a quantitative version of the inverse function theorem thus given a finite map we use local height functions to describe how far away from the ramification locus

a new algorithm for two finite families of demicontractive mappings and equilibrium problems in this paper we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings the strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real hilbert space our result generalizes several recent results in the current literature

fixed point results for a generalized nonexpansive map in uniformly convex metric spaces abstract in this paper the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved this fixed point is approximated by averaging krasnosel skii iterations of a generalized nonexpansive map our results substantially improve and extend several known results existing in the literature

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

positive solutions of second order differential equations we prove a nonoscillation result for second order nonlinear ordinary differential equations an application to the schrodinger equation is also given c 2004 elsevier ltd all rights reserved

the mordell lang conjecture for function fields we give a proof of the geometric mordell lang conjecture in any characteristic our method involves a model theoretic analysis of the kernel of manin s homomorphism and of a certain analog in characteristic p department of mathematics massachusetts institute of technology 2 277 cambridge massachusetts 02139 current address department of mathematics hebrew university jerusalem israel e mail address ehud math mit edu

strong convergence of a general iteration scheme in cat 0 spaces abstract we introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi nonexpansive maps in convex metric spaces and c a t 0 spaces the new iteration scheme includes modified mann and ishikawa iterations the three step iteration scheme of xu and noor and the scheme of khan domlo and fukhar ud din as special cases in banach spaces our results are refinements and generalizations of several recent results from the current literature

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

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

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling abstract this article investigates both basic qualitative and basic quantitative properties of solutions to first and higher order dynamic equations on time scales and thus provides a foundation and framework for future advanced nonlinear studies in the field particular focus lies in the existence uniqueness dependency approximation and explicit representation of solutions to nonlinear initial value problems the main tools used are from modern areas of nonlinear analysis including the fixed point theorems of banach and schafer the method of successive approximations a novel definition of measuring distance in metric spaces and normed spaces and a separation of variables technique is introduced to the general time scale setting the new results compliment and extend those of stefan hilger s seminal paper of 1990 as an application of the new results we present and analyse a simple model from economics known as the keynesian cross model with lagged income in the general time scale environment ideas suggesting further applications and possible new directions for the novel results are also presented

the brauer manin obstruction for subvarieties of abelian varieties over function fields we prove that for a large class of subvarieties of abelian varieties over global function fields the brauer manin condition on adelic points cuts out exactly the rational points this result is obtained from more general results concerning the intersection of the adelic points of a subvariety with the adelic closure of the group of rational points of the abelian variety

weak and strong convergence theorems for nonspreading type mappings in hilbert spaces abstract weak and strong convergence theorems are proved in real hilbert spaces for a new class of nonspreading type mappings more general than the class studied recently in kurokawa and takahashi y kurokawa w takahashi weak and strong convergence theorems for nonspreading mappings in hilbert spaces nonlinear anal 73 2010 1562 1568 we explored an auxiliary mapping in our theorems and proofs and this also yielded a strong convergence theorem of halpern s type for our class of mappings and hence resolved in the affirmative an open problem posed by kurokawa and takahashi in their final remark for the case where the mapping t is averaged

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

basic existence uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales abstract this paper focuses on the qualitative and quantitative properties of solutions to certain nonlinear dynamic equations on time scales we present some new sufficient conditions under which these general equations admit a unique positive solution these positive and hence non oscillatory solutions extend across unbounded intervals and tend to a finite limit as the independent variable becomes large and positive our methods include banach s fixed point theorem including the method of picard iterations and weighted norms and metrics in the time scale setting due to the wide ranging nature of dynamic equations on time scales our results are novel for ordinary differential equations for difference equations for combinations of the two areas and for general time scales this is demonstrated via some examples furthermore we state an open problem of interest

absolute continuity and existence of solutions to dynamic inclusions in time scales we provide some properties for absolutely continuous functions in time scales then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question we also introduce the so called euler solution to dynamical systems in time scales and prove its existence a combination of the existence of euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty compact convex and has closed graph