fixed point iterations for asymptotically nonexpansive mappings in banach spaces in this paper we suggest and analyze a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces the new iterative scheme includes ishikawa type and mann type interations as special cases the results obtained in this paper represent an extension as well as refinement of previous known results

fixed point iterations for certain nonlinear mappings abstract in a recent paper schu established the convergence of the mann iterates of a completely continuous asymptotically nonexpansive mapping on a hilbert space in this paper we extend the result of schu to uniformly convex spaces we also obtain the same generalization for the ishikawa iteration process

ambrosetti prodi type multiplicity result for a wave equation with sublinear nonlinearity abstract we shall prove a weakened ambrosetti prodi type multiplicity result for a wave equation with sublinear nonlinearity and without damping due to infinite dimensional kernel of the wave operator the leray schauder and coincidence degrees are not available we use an extension of the leray schauder degree to obtain multiple solutions

a proof of sudakov theorem with strictly convex norms the paper establishes a solution to the monge problem in mathbb r n for a possibly asymmetric norm cost function and absolutely continuous initial measures under the assumption that the unit ball is strictly convex but not necessarily differentiable nor uniformly convex the proof follows the strategy initially proposed by sudakov in 1976 found to be incomplete in 2000 the missing step is fixed in the above case adapting a disintegration technique introduced for a variational problem by strict convexity mass moves along rays and we also investigate the divergence of the vector field of rays

an ambrosetti prodi type result for periodic solutions of the telegraph equation using leray schander degree theory a theorem of upper and lower solutions and a strong maximum principle for the telegraph equation we prove an ambrosetti prodi type result for periodic solutions of the telegraph equation

on a singular periodic ambrosetti prodi problem abstract we investigate the possibility of extending a classical multiplicity result by fabry mawhin and nkashama to a periodic problem of ambrosetti prodi type having a nonlinearity with possibly one or two singularities in the second part of the paper we study the existence of periodic rotating solutions for radially symmetric systems with nonlinearities of the same type

fixed point iteration processes for asymptotic pointwise nonexpansive mappings in banach spaces abstract let x be a uniformly convex banach space with the opial property let t c c be an asymptotic pointwise nonexpansive mapping where c is bounded closed and convex subset of x in this paper we prove that the generalized mann and ishikawa processes converge weakly to a fixed point of t in addition we prove that for compact asymptotic pointwise nonexpansive mappings acting in uniformly convex banach spaces both processes converge strongly to a fixed point

constructing optimal maps for monge s transport problem as a limit of strictly convex costs the monge kantorovich problem is to move one distribution of mass onto another as efficiently as possible where monge s original criterion for efficiency 19 was to minimize the average distance transported subsequently studied by many authors it was not until 1976 that sudakov showed solutions to be realized in the original sense of monge i e as mappings from rn to rn 23 a second proof of this existence result formed the subject of a recent monograph by evans and gangbo 7 who avoided sudakov s measure decomposition results by using a partial differential equations approach in the present manuscript we give a third existence proof for optimal mappings which has some advantages and disadvantages relative to existing approaches it requires no continuity or separation of the mass distributions yet our explicit construction yields more geometrical control than the abstract method of sudakov indeed this control turns out to be essential for addressing a gap which has recently surfaced in sudakov s approach to the problem in dimensions n 3 see the remarks at the end of this section it is also shorter and more flexible than either and can be adapted to handle transportation on riemannian manifolds or around obstacles as we plan to show in a subsequent work 13 the problem considered here is the classical one problem 1 monge fix a norm d x y llx yll on rn and two densities non negative borel functions f fe ll rn satisfying the mass balance condition

the monge problem for distance cost in geodesic spaces we address the monge problem in metric spaces with a geodesic distance x d is a polish space and dl is a geodesic borel distance which makes x dl a non branching geodesic space we show that under the assumption that geodesics are d continuous and locally compact we can reduce the transport problem to 1 dimensional transport problems along geodesics we introduce two assumptions on the transport problem which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w r t the 1 dimensional hausdorff distance induced by dl it is known that this regularity is sufficient for the construction of a transport map we study also the dynamics of transport along the geodesic the stability of our conditions and show that in this setting dl cyclical monotonicity is not sufficient for optimality

asymptotic pointwise contractions a simple and elementary without using the ultrapower technique proof for the existence of a fixed point of an asymptotic pointwise contraction is provided the existence of fixed points for asymptotic pointwise nonexpansive mappings in a uniformly convex banach space is also investigated

monge problem in metric measure spaces with riemannian curvature dimension condition abstract we prove the existence of solutions for the monge minimization problem addressed in a metric measure space x d m enjoying the riemannian curvature dimension condition rcd k n with n for the first marginal measure we assume that 0 m as a corollary we obtain that the monge problem and its relaxed version the monge kantorovich problem attain the same minimal value moreover we prove a structure theorem for d cyclically monotone sets neglecting a set of zero m measure they do not contain any branching structures that is they can be written as the disjoint union of the image of a disjoint family of geodesics

existence of optimal transport maps for crystalline norms we show the existence of optimal transport maps in the case when the cost function is the distance induced by a crystalline norm in n assuming that the initial distribution of mass is absolutely continuous with respect to mathcal l n the proof is based on a careful decomposition of the space in transport rays induced by a secondary variational problem having the euclidean distance as cost function moreover improving a construction by larman we show the existence of a nikodym set in 3 having full measure in the unit cube intersecting each element of a family of pairwise disjoint open lines only in one point this example can be used to show that the regularity of the decomposition in transport rays plays an essential role in sudakov type arguments for proving the existence of optimal transport maps

radially symmetric systems with a singularity and asymptotically linear growth abstract we prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type the nonlinearity is assumed to have a linear growth at infinity being controlled by two constants which have a precise interpretation in terms of the dancer fucik spectrum our result generalizes an existence theorem by del pino et al 1992 4 obtained in the case of a scalar second order differential equation

evolution monge kantorovich equation abstract the paper deals with monge kantorovich equation mk for short in an open bounded domain with dirichlet boundary condition we study existence and uniqueness of a solution to the associated evolution problem emk for short and we prove the convergence to a solution of mk when time goes to a solution is a couple u where u is the potential and is the transportation flux we study the problem for a given radon measure source term and we show how to use the numerical method of dumont and igbida 2009 22 to provide numerical approximation of the solution of mk

a study of the dual problem of the one dimensional l infinity optimal transport problem with applications the monge kantorovich problem for the infinite wasserstein distance presents several peculiarities among them the lack of convexity and then of a direct duality we study in dimension 1 the dual problem introduced by barron bocea and jensen we construct a couple of kantorovich potentials which is as less trivial as possible more precisely we build a potential which is non constant around any point that the plan which is locally optimal moves at maximal distance as an application we show that the set of points which are displaced to maximal distance by a locally optimal transport plan is minimal

periodic orbits of radially symmetric keplerian like systems a topological degree approach abstract we are concerned with non autonomous radially symmetric systems with a singularity which are t periodic in time by the use of topological degree theory we prove the existence of large amplitude periodic solutions whose minimal period is an integer multiple of t precise estimates are then given in the case of keplerian like systems showing some resemblance between the orbits of those solutions and the circular orbits of the corresponding classical autonomous system

on asymptotic pointwise nonexpansive mappings in modular function spaces we prove the existence of fixed points of asymptotic pointwise nonexpansive mappings in modular function spaces

on the superlinear ambrosetti prodi problem l et be a smooth bounded domain in r n we consider the semilinear elliptic boundary value problem

optimal transport with convex obstacle we consider the monge transportation problem when the cost is the squared geodesic distance around a convex obstacle we show that there exists at least one and in general infinitely many optimal transport maps

a characterization for solutions of the monge kantorovich mass transport problem a measure theoretical approach is presented to study the solutions of the monge kantorovich optimal mass transport problems this approach together with kantorovich duality provide an effective tool to answer a long standing question about the support of optimal plans for the mass transport problem involving general cost functions we also establish a criterion for the uniqueness

continuity for the monge mass transfer problem in two dimensions in this paper we prove the continuity of the monotone optimal mapping of the monge mass transfer problem in two dimensions under certain conditions on the domains and the mass distributions

viscosity solutions of minimization problems viscosity methods for minimization problems are revisited from some modern perspectives in variational analysis variational convergences for sequences of functions epi convergence gamma convergence mosco convergence and for sequences of operators graph convergence provide a flexible tool for such questions it is proved in a rather large setting that the solutions of the approximate problems converge to a viscosity solution of the original problem that is a solution that is minimal among all the solutions with respect to some viscosity criteria various examples coming from mathematical programming calculus of variations semicoercive elliptic equations phase transition theory hamilton jacobi equations singular perturbations and optimal control theory are considered