impacts of noise on a class of partial differential equations abstract this paper is concerned with effects of noise on the solutions of partial differential equations we first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic partial differential equations then we prove that noise could induce singularities finite time blow up of solutions finally we show that a stochastic allen cahn equation does not have finite time singularities and the unique solution exists globally

yosida approximations for multivalued stochastic partial differential equations driven by levy noise on a gelfand triple abstract we prove the existence and uniqueness of solutions for a class of multivalued stochastic partial differential equations with maximal monotone drift on banach space driven by multiplicative levy noise we also establish the strong convergence result for solutions of the approximating equations where the maximal monotone drift operator is replaced by its yosida approximation as an application the existence and uniqueness of solutions for multivalued stochastic porous medium equations is obtained

existence of optimal controls for spde with locally monotone coefficients the aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations spdes with locally monotone coefficients controlled by

asymptotic couplings by reflection and applications for nonlinear monotone spdes abstract asymptotic couplings by reflection are constructed for a class of nonlinear monotone spdes stochastic partial differential equations as applications gradient holder estimates as well as exponential convergence are derived for the associated markov semigroup the main results are illustrated by stochastic generalized porous media equations stochastic p laplacian equations and stochastic generalized fast diffusion equations we emphasize that the gradient estimate is studied for the first time for these equations

on strictly positively invariant cones for a matrix a rn n it is shown that strict positive invariance of a proper cone c rn that is etac 0 int c t 0 implies the existence of a certain direct sum decomposition of rn into a invariant subspaces our results lead to a characterization of the set of initial points which give rise to solution curves that reach s under the differential equation ax also given is an application in stability theory

random attractors for singular stochastic evolution equations abstract the existence of random attractors for singular stochastic evolution equations see perturbed by general additive noise is proven the drift is only assumed to satisfy the standard assumptions of the variational approach to see with compact embeddings in the gelfand triple and singular coercivity for ergodic monotone contractive random dynamical systems it is proven that the random attractor consists of a single random point in case of real linear multiplicative noise finite time extinction is obtained applications include stochastic generalized fast diffusion equations and stochastic generalized singular p laplace equations perturbed by levy noise with jump measure having finite first and second moments

numerical experiments in 2 d ihcp on bounded domains part i the interior cube problem abstract different space marching implementations of the mollification method are introduced to numerically recover the temperature and heat flux histories at interior points of bounded subdomains of a finite two dimensional rectangular body when the temperature and heat flux functions are approximately measured at one boundary side

some p properties for linear transformations on euclidean jordan algebras a real square matrix is said to be a p matrix if all its principal minors are positive it is well known that this property is equivalent to the nonsign reversal property based on the componentwise product of vectors the order p property based on the minimum and maximum of vectors uniqueness property in the standard linear complementarity problem lipschitzian homeomorphism property of the normal map corresponding to the nonnegative orthant in this article we extend these notions to a linear transformation defined on a euclidean jordan algebra we study some interconnections between these extended concepts and specialize them to the space s n of all n n real symmetric matrices with the semidefinite cone s n and to the space r n with the lorentz cone

existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions abstract in this paper we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions which can be applied to a large class of spde with finite delays e g d dimensional stochastic fractional navier stokes equations with delays d dimensional stochastic reaction diffusion equations with delays d dimensional stochastic porous media equations with delays moreover under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to spde with delays

extension of primal dual interior point algorithms to symmetric cones in this paper we show that the so called commutative class of primal dual interior point algorithms which were designed by monteiro and zhang for semidefinite programming extends word for word to optimization problems over all symmetric cones the machinery of euclidean jordan algebras is used to carry out this extension unlike some non commutative algorithms such as the xs sx method this class of extensions does not use concepts outside of the euclidean jordan algebras in particular no assumption is made about representability of the underlying jordan algebra as a special case we prove polynomial iteration complexities for variants of the short semi long and long step path following algorithms using the nesterov todd xs or sx directions

stochastic porous media equations and self organized criticality the existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and wiener forcing term is proven the finite time extinction of solutions with high probability is also proven in 1 d the results are relevant for self organized criticality behavior of stochastic nonlinear diffusion equations with critical states

spde in hilbert space with locally monotone coefficients the aim of this paper is to extend the usual framework of spde with monotone coecients to include a large class of cases with merely locally monotone coecients this new framework is conceptually not more involved than the classical one but includes many more fundamental examples not included previously thus our main result can be applied to various types of spdes such as stochastic reaction diusion equations stochastic burgers type equation stochastic 2 d navier stokes equation stochastic p laplace equation and stochastic porous media equation with non monotone perturbations

travelling waves for reaction diffusion equations forced by translation invariant noise abstract inspired by applications we consider reaction diffusion equations on r that are stochastically forced by a small multiplicative noise term that is white in time coloured in space and invariant under translations we show how these equations can be understood as a stochastic partial differential equation spde forced by a cylindrical q wiener process and subsequently explain how to study stochastic travelling waves in this setting in particular we generalize the phase tracking framework that was developed in hamster and hupkes 2018 2019 for noise processes driven by a single brownian motion the main focus lies on explaining how this framework naturally leads to long term approximations for the stochastic wave profile and speed we illustrate our approach by two fully worked out examples which highlight the predictive power of our expansions

random attractors for a class of stochastic partial differential equations driven by general additive noise abstract the existence of random attractors for a large class of stochastic partial differential equations spde driven by general additive noise is established the main results are applied to various types of spde as e g stochastic reaction diffusion equations the stochastic p laplace equation and stochastic porous media equations besides classical brownian motion we also include space time fractional brownian motion and space time levy noise as admissible random perturbations moreover cases where the attractor consists of a single point are also investigated and bounds for the speed of attraction are obtained

weak solution of a stochastic 3d cahn hilliard navier stokes model driven by jump noise abstract we investigate a stochastic 2d and 3d cahn hilliard navier stokes system with a multiplicative noise of levy type the model consists of the navier stokes equations for the velocity coupled with a cahn hilliard system for the order phase parameter we prove that the system the existence of weak martingale solution for both 2d and 3d cases the proof of the existence is based on a classical galerkin approximation as well as some compactness methods in the 2d case we prove the pathwise uniqueness of the weak solution

strong solutions for a stochastic model of two dimensional second grade fluids driven by levy noise abstract in this paper we consider stochastic second grade fluids driven by levy noise on a bounded domain of r 2 global existence and uniqueness of strong probabilistic solutions are established which improves the existing corresponding results for martingale solutions in literature

freidlin wentzell s large deviations for stochastic evolution equations abstract we prove a freidlin wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises in particular our general result can be used to deal with a large class of quasi linear stochastic partial differential equations such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and p laplacian second order term

generalizations of m matrices which may not have a nonnegative inverse abstract generalizations of m matrices are studied including the new class of gm matrices the matrices studied are of the form si b with b having the perron frobenius property but not necessarily being nonnegative results for these classes of matrices are shown which are analogous to those known for m matrices also various splittings of a gm matrix are studied along with conditions for their convergence

well posedness of stochastic partial differential equations with lyapunov condition abstract in this paper we show the existence and uniqueness of strong solutions for a large class of spde where the coefficients satisfy the local monotonicity and lyapunov condition one sided linear growth condition moreover some new invariance result and stronger regularity estimate are also established for the solutions as examples the main result is applied to stochastic tamed 3d navier stokes equations stochastic generalized curve shortening flow singular stochastic p laplace equations stochastic fast diffusion equations stochastic burgers type equations and stochastic reaction diffusion equations

complementarity forms of theorems of lyapunov and stein and related results abstract the well known lyapunov s theorem in matrix theory continuous dynamical systems asserts that a complex square matrix a is positive stable i e all eigenvalues lie in the open right half plane if and only if there exists a positive definite matrix x such that ax xa is positive definite in this paper we prove a complementarity form of this theorem a is positive stable if and only if for any hermitian matrix q there exists a positive semidefinite matrix x such that ax xa q is positive semidefinite and x ax xa q 0 by considering cone complementarity problems corresponding to linear transformations of the form i s we show that a complex matrix a has all eigenvalues in the open unit disk of the complex plane if and only if for every hermitian matrix q there exists a positive semidefinite matrix x such that x axa q is positive semidefinite and x x axa q 0 by specializing q to i we deduce the well known stein s theorem in discrete linear dynamical systems a has all eigenvalues in the open unit disk if and only if there exists a positive definite matrix x such that x axa is positive definite

an optimal modified method for a two dimensional inverse heat conduction problem we consider a two dimensional inverse heat conduction problem which is severely ill posed i e the solution if it exists does not depend continuously on the data from the frequency domain we propose an optimal modified method to solve the problem in the presence of noisy data we give and prove the optimal convergence estimate which shows that the regularized solution is dependent continuously on the data and is an approximation of the exact solution of the two dimensional inverse heat conduction problem

the linear order complementarity problem the classical complementarity problem in euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem generalizations of the former have been extensively studied but infinite dimensional analogues of the latter have been largely ignored moreover as we show many well known results about the classical complementarity problem are more appropriately viewed order theoretically this is particularly true of least element solutions which are central to the present study of order complementarity in vector lattices we emphasize that the lattice theoretic descriptions we employ are very useful even in the standard finite dimensional setting

stochastic generalized porous media and fast diffusion equations abstract we present a generalization of krylov rozovskii s result on the existence and uniqueness of solutions to monotone stochastic differential equations as an application the stochastic generalized porous media and fast diffusion equations are studied for finite reference measures where the drift term is given by a negative definite operator acting on a time dependent function which belongs to a large class of functions comparable with the so called n functions in the theory of orlicz spaces

well posedness and invariant measures for a class of stochastic 3d navier stokes equations with damping driven by jump noise abstract a class of stochastic 3d navier stokes equation with damping driven by a noise of levy type is considered in this paper the existence and uniqueness of the solution for the problem 1 1 1 2 are proved for 2 with any 0 and 1 4 as 2 the main result covered various types of spde such as stochastic 3d navier stokes equations with damping stochastic tamed 3d navier stokes equations stochastic three dimensional brinkman forchheimer extended darcy model by using the exponential stability of solutions the existence of a unique invariant measures is proved

on the bilinearity rank of a proper cone and lyapunov like transformations a real square matrix q q is a bilinear complementarity relation on a proper cone k k in mathbb r n r n if begin aligned x in k s in k text and langle x s rangle 0 rightarrow x t qs 0 end aligned x k s k and x s 0 x t q s 0 where k k is the dual of k k the bilinearity rank of k k is the dimension of the linear space of all bilinear complementarity relations on k k in this article we continue the study initiated by rudolf et al math prog ser b 129 5 31 2011 we show that bilinear complementarity relations are related to lyapunov like transformations that appear in dynamical systems and in complementarity theory and further show that the bilinearity rank of k k is the dimension of the lie algebra of the automorphism group of k k in addition we correct a result of rudolf et al compute the bilinearity ranks of symmetric and completely positive cones and state some schur type results for lyapunov like transformations

stochastic tamed 3d navier stokes equations existence uniqueness and ergodicity in this paper we prove the existence of a unique strong solution to a stochastic tamed 3d navier stokes equation in the whole space as well as in the periodic boundary case then we also study the feller property of solutions and prove the existence of invariant measures for the corresponding feller semigroup in the case of periodic conditions moreover in the case of periodic boundary and degenerated additive noise using the notion of asymptotic strong feller property proposed by hairer and mattingly ann math 164 993 1032 2006 we prove the uniqueness of invariant measures for the corresponding transition semigroup

wong zakai approximation and support theorem for spdes with locally monotone coefficients abstract in this paper we present the wong zakai approximation results for a class of nonlinear spdes with locally monotone coefficients and driven by multiplicative wiener noise this model extends the classical monotone one and includes examples like stochastic 2d navier stokes equations stochastic porous medium equations stochastic p laplace equations and stochastic reaction diffusion equations as a corollary our approximation results also describe the support of the distribution of solutions

martingale and weak solutions for a stochastic nonlocal burgers equation on finite intervals abstract this work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal burgers equation on a one dimensional bounded domain the existence of a martingale solution is shown by using a galerkin approximation prokhorov s theorem and skorokhod s embedding theorem the same galerkin approximation also leads to the existence of weak solution for the corresponding deterministic nonlocal burgers equation on a bounded domain

extended m matrices and subtangentiality the concept of a singular m matrix a with respect to a proper cone x is extended by replacing the usual regularity condition a al b for a xnonnegative matrix b with the weaker condition exponential nonnegativity of a as in earlier work which dealt with the nonsingular case in the present characterizations the lack of regularity is overcome by employing subtangentiality

on the game theoretic value of a linear transformation relative to a self dual cone this paper is concerned with a generalization of the concept of value of a zero sum matrix

z transformations on proper and symmetric cones z transformations motivated by the similarities between the properties of z matrices on r n and lyapunov and stein transformations on the semidefinite cone mathcal s n we introduce and study z transformations on proper cones we show that many properties of z matrices extend to z transformations we describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations finally we study the equivalence of q and p properties of z transformations on symmetric cones in particular we prove such an equivalence on the lorentz cone

harnack inequality and applications for stochastic generalized porous media equations by using coupling and girsanov transformations the dimension free harnack inequality and the strong feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations as applications explicit upper bounds of the l p norm of the density as well as hypercontractivity ultracontractivity and compactness of the corresponding semigroup are derived

harnack inequality and strong feller property for stochastic fast diffusion equations abstract as a continuation to f y wang harnack inequality and applications for stochastic generalized porous media equations ann probab 35 2007 1333 1350 where the harnack inequality and the strong feller property are studied for a class of stochastic generalized porous media equations this paper presents analogous results for stochastic fast diffusion equations since the fast diffusion equation possesses weaker dissipativity than the porous medium one does some technical difficulties appear in the study as a compensation to the weaker dissipativity condition a sobolev nash inequality is assumed for the underlying self adjoint operator in applications some concrete examples are constructed to illustrate the main results

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

random attractors for locally monotone stochastic partial differential equations abstract we prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive levy noise the main result is applicable to various types of spde such as stochastic burgers type equations stochastic 2d navier stokes equations the stochastic 3d leray model stochastic power law fluids the stochastic ladyzhenskaya model stochastic cahn hilliard type equations stochastic kuramoto sivashinsky type equations stochastic generalized porous media equations and stochastic generalized p laplace equations

almost sure asymptotic stability of stochastic partial differential equations with jumps in this paper we investigate stochastic partial differential equations with jumps in infinite dimensions the key motivation of this paper is under a local lipschitz condition but without a linear growth condition to give an existence and uniqueness theorem khasminskii type theorem where the classical existence and uniqueness result can be regarded as a special case and then to discuss the almost sure asymptotic stability of the solutions moreover as a by product we also derive that the solutions are weakly attracted finally several examples are constructed to demonstrate our results

some inertia theorems in euclidean jordan algebras abstract this paper deals with some inertia theorems in euclidean jordan algebras first based on the continuity of eigenvalues we give an alternate proof of kaneyuki s generalization of sylvester s law of inertia in simple euclidean jordan algebras as a consequence we show that the cone spectrum of any quadratic representation with respect to a symmetric cone is finite second we present ostrowski schneider type inertia results in euclidean jordan algebras in particular we relate the inertias of objects a and x in a euclidean jordan algebra when l a x 0 or s a x 0 where l a and s a denote lyapunov and stein transformations respectively

existence and uniqueness of solutions to nonlinear evolution equations with locally monotone operators abstract in this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on a banach space with locally monotone operators which is a generalization of the classical result for monotone operators in particular we show that local monotonicity implies pseudo monotonicity the main results are applied to pde of various types such as porous medium equations reaction diffusion equations the generalized burgers equation the navier stokes equation the 3d leray model and the p laplace equation with non monotone perturbations

on the p property of z and lyapunov like transformations on euclidean jordan algebras abstract the p z and s properties of a linear transformation on a euclidean jordan algebra are generalizations of the corresponding properties of a square matrix on rn motivated by the equivalence of p and s properties for a z matrix 2 and a similar result for lyapunov and stein transformations on the space of real symmetric matrices 6 5 in this paper we present two results supporting the conjecture that p and s properties are equivalent for a z transformation on a euclidean jordan algebra we show that the conjecture holds for lyapunov like transformations and z transformations satisfying an additional condition

existence of strong solutions for stochastic porous media equation under general monotonicity conditions this paper addresses existence and uniqueness of strong solutions to stochastic porous media equations dx x dt b x dw t in bounded domains of r d with dirichlet boundary conditions here is a maximal monotone graph in r r possibly multivalued with

local and global well posedness of spde with generalized coercivity conditions abstract in this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions an analogous result is obtained for stochastic evolution equations in hilbert space with additive noise as applications the main results are applied to obtain simpler proofs in known cases as the stochastic 3d navier stokes equation the tamed 3d navier stokes equation and the cahn hilliard equation but also to get new results for stochastic surface growth pde and stochastic power law fluids

some p properties for nonlinear transformations on euclidean jordan algebras in this article we introduce the concepts of p and p0 properties for a nonlinear transformation defined on a euclidean jordan algebra and study existence of solution in the associated complementarity problems in particular we show in this general setting that if a transformation has the p0 and r0 properties then all associated complementarity problems have solutions we also describe a necessary condition for a transformation to have the global uniqueness of solution property

large deviation problem for some parabolic itǒ equations the large deviation problem of wentzell freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise in a hilbert space setting it is proved that under suitable conditions the associated family of solution measures depending on a small parameter obeys the large deviation principle with respect to a certain rate function

non monotone stochastic generalized porous media equations abstract by using the nash inequality and a monotonicity approximation argument existence and uniqueness of strong solutions are proved for a class of non monotone stochastic generalized porous media equations moreover we prove for a large class of stochastic pde that the solutions stay in the smaller l 2 space provided the initial value does so that some recent results in the literature are considerably strengthened

large deviations for stochastic porous media equation on general measure spaces abstract in this paper we establish a large deviation principle for stochastic porous media equations driven by time dependent multiplicative noise on a finite measure space e b e and with the laplacian replaced by a negative definite self adjoint operator the coefficient is only assumed to satisfy the increasing lipschitz nonlinearity assumption without the restriction r r as r for l 2 initial data this paper also gets rid of the compact embedding assumption on the associated gelfand triple examples of the negative definite self adjoint operators include fractional powers of the laplacian i e l 0 1 generalized schr o dinger operators i e l 2 and laplacians on fractals

a multiscale analysis of stochastic bistable reaction diffusion equations abstract a multiscale analysis of 1d stochastic bistable reaction diffusion equations with additive noise is carried out w r t travelling waves within the variational approach to stochastic partial differential equations it is shown with explicit error estimates on appropriate function spaces that up to lower order w r t the noise amplitude the solution can be decomposed into the orthogonal sum of a travelling wave moving with random speed and into gaussian fluctuations a stochastic differential equation describing the speed of the travelling wave and a linear stochastic partial differential equation describing the fluctuations are derived in terms of the coefficients our results extend corresponding results obtained for stochastic neural field equations to the present class of stochastic dynamics

on some interconnections between strict monotonicity globally uniquely solvable and p properties in semidefinite linear complementarity problems in the setting of semidefinite linear complementarity problems on sn the implications strict monotonicity p2 gus p are known here p and p2 properties for a linear transformation l sn sn are respectively defined by x sn xl x l x x 0 x 0 and x 0 y 0 x y l x l y x y 0 x y gus refers to the global unique solvability in semidefinite linear complementarity problems correspond ing to l in this article we show that the reverse implications hold for any self adjoint linear transformation and for normal lyapunov and stein transformations by introducing the concept of a principal subtransformation of a linear transformation we show that l sn sn has the p2 property if and only if for every n n real invertible matrix q every principal subtransformation of l has the p property where l x qtl qxqt q based on this we show that p2 gus and p properties coincide for the two sided multiplication transfor mation

minimum eigenvalue inequalities for z transformations on proper and symmetric cones abstract a linear transformation l defined on a finite dimensional real hilbert space is said to be a z transformation on a proper cone k if x k y k and x y 0 l x y 0 where k is the dual of k examples of such transformations include z matrices on r n lyapunov and stein transformations on the semidefinite cone for a z transformation l l min l is an eigenvalue of l with a corresponding eigenvector in k in this article when k is a product cone we relate the z property positive stable property minimum real eigenvalue of l with those of a subtransformation of l and its schur complement

on the block norm p property a real n n matrix m is said to be a p matrix if all its principal minors are positive in a recent paper chua and yi 2 described this property in terms of norm there exists a 0 such that for all nonnegative diagonal matrices d and vectors x mx dx x in this paper we introduce a block version of this property for a linear transformation defined on a product of normed or inner product spaces in addition to relating this to real positive stability and positive principal minor properties we study the invariance of this property by principal subtransformations and schur complements we also specialize this property to z transformations and to euclidean jordan algebras

on the existence and uniqueness of solution to a stochastic 2d cahn hilliard navier stokes model abstract we study in this article a stochastic version of a coupled cahn hilliard navier stokes model in a two dimensional bounded domain the model consists of the navier stokes equations for the velocity coupled with a cahn hilliard model for the order phase parameter we prove the existence and the uniqueness of a variational solution

some results on a partition of z matrices fiedler and markham define an n n matrix a to be an lk matrix if a has the form a ti b where b is nonnegative and k b t k 1 b k 1 2 n here k b denotes the maximum spectral radius of all principal submatrices of b of order k for k 1 2 n and for completeness n 1 b is defined to be further a is defined to be an l0 matrix if a ti b where b is nonnegative and t 1 b the classes l0 l1 ln form a partition of the class of z matrices in this paper we characterize nonsingular matrices in these classes in terms of the principal minors of their inverses and extend this characterization to general lk matrices inverse lk matrices and schur complements of lk matrices are also studied an eigenvalue inequality involving schur complements of lk matrices is obtained

on the stochastic p laplace equation the p laplace equation with random perturbation is studied for the singular case 1 p 2 in this paper some properties of the invariant measure and transition semigroups are obtained the main tool is the dimension free harnack inequality which is established by using the coupling argument as consequences some ergodicity compactness and contractive properties are derived for the associated transition semigroups the main results are applied to stochastic reaction diffusion equations and the stochastic p laplace equation in hilbert space

generalized m matrices abstract let r n be a proper cone from the theory of m matrices see e g 1 it is known that if there exist 0 and a matrix b such that a b i then the following conditions are equivalent i a is monotone ii a is seminegative iii re spectrum a e ta t 0 is more general than the structural assumption a b i conditions i iii are nevertheless all equivalent to iv x ax 0 when e holds

solving an ill posed cauchy problem for a two dimensional parabolic pde with variable coefficients using a preconditioned gmres method the sideways parabolic equation spe is a model of the problem of determining the temperature on the surface of a body from the interior measurements mathematically it can be formulated as a noncharacteristic cauchy problem for a parabolic partial differential equation this problem is severely ill posed in an l 2 setting we use a preconditioned generalized minimum residual method gmres to solve a two dimensional spe with variable coefficients the preconditioner is singular and chosen in a way that allows efficient implementation using the fft the preconditioner is a stabilized solver for a nearby problem with constant coefficients and it reduces the number of iterations in the gmres algorithm significantly numerical experiments are performed that demonstrate the performance of the proposed method

generalized m matrices and ordered banach algebras abstract a matrix a r n n is an m matrix if and only if the mapping x ax is quasimonotone increasing qmi and if the right spectral bound of a is negative here qmi is meant with respect to the natural cone k x r n x k 0 one possibility of generalizing m matrices is to consider qmi linear mappings on r n with respect to other cones k r n we will present results on such mappings in the banach algebra setting and discuss some special cones moreover by means of one sided estimates it is possible to get informations on the right spectral bound of qmi mappings