strong convergence for the modified mann s iteration of λ strict pseudocontraction abstract in this paper for an strict pseudocontraction t we prove strong convergence of the modified mann s iteration defined by x n 1 n u n x n 1 n n n tx n 1 n x n where n n and n in 0 1 satisfy i 0 n k 2 with lim inf n n k 2 n 0 ii lim n n 0 and n 1 n iii lim sup n n 1 our results unify and improve some existing results

lim inf convergence in partially ordered sets the lim inf convergence in a complete lattice was introduced by scott to characterize continuous lattices here we introduce and study the lim inf convergence in a partially ordered set the main result is that for a poset p the lim inf convergence is topological if and only if p is a continuous poset a weaker form of lim inf convergence in posets is also discussed

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

an approach to fuzzy frames via fuzzy posets in this paper based on a complete heyting algebra l we define a fuzzy version of frames called l frames then we construct an adjunction between the category of stratified l topological spaces and that of l locales the opposite category of l frames which is a fuzzy counterpart of the isbell adjunction between topological spaces and locales we also study the corresponding sobriety of stratified l topologies and spatiality of l frames and show the dual equivalence between them

the l ordered semigroups based on l partial orders abstract fuzzy frame valued ordered semigroups are investigated with the orders being l partial orders in this framework l left resp l right ideals l bi ideals and l quasi ideals of an l ordered semigroup are discussed the idea of which is applied to the characterizations of regular and duo l ordered semigroups in addition the relationship between an l ordered semigroup and an l topological semigroup is studied as a consequence an isomorphism between the category of l ordered semigroups and the category of l topological semigroups with the topologies being l t 0 and alexandrov is obtained

stability and bifurcation analysis for a discrete time model of lotka volterra type with delay a discrete model of lotka volterra type with delay is considered and a bifurcation analysis is undertaken for the model we derive the precise conditions ensuring the asymptotic stability of the positive equilibrium with respect to two characteristic parameters of the system it is shown that for certain values of these parameters fold or neimark sacker bifurcations occur but codimension 2 fold neimark sacker double neimark sacker and resonance 1 1 bifurcations may also be present the direction and the stability of the neimark sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory

convergence theorems of fixed points for κ strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t c h is a strict pseudo contraction such that f t x c x t x 0 consider the normal mann s iterative algorithm given by x 1 c x n 1 n x n 1 n p c s x n n 1 where s c h is defined by s x x 1 t x p c is the metric projection of h onto c and n n 1 for all n 1 it is proved that if the control parameter sequence n is chosen so that n 1 and n 1 n 1 n then x n converges weakly to a fixed point of t in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c the results presented in this article respectively improve and extend the recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 349 from strictly pseudo contractive self mappings to nonself mappings and of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 from nonexpansive mappings to strict pseudo contractions

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a 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 mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

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

convergence theorems of common fixed points for a finite family of lipschitz pseudocontractions in banach spaces abstract in this paper we continue to study weak convergence problems for the implicit iteration process for a finite family of lipschitzian continuous pseudocontractions in general banach spaces the results presented in this paper improve and extend the corresponding ones of xu and ori h k xu r g ori an implicit iteration process for nonexpansive mappings numer funct anal optim 22 2001 767 773 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 chen et al r chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 and others

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

dynamics of numerical discretization in a delayed diffusive nicholson s blowflies equation in this article we study the dynamics of a diffusive nicholson s blowflies equation with a finite delay and dirichlet boundary condition by the forward and backward euler difference schemes and crank nicolson scheme the existence of hopf bifurcation at the equilibrium is obtained through analyzing the distribution of the eigenvalues we find that the unstable equilibrium state without dispersion may become stable with dispersion under certain conditions our results show that crank nicolson and the backward euler difference schemes are superior to the forward euler difference scheme under the means of describing approximately the dynamics of the original system finally numerical examples are provided to illustrate the analytical results

a stone type duality for st0 stratified alexandrov l topological spaces abstract we show that for every complete lattice a both the set of completely prime elements and the set of completely coprime elements are one to one corresponding to ch a the set of complete lattice homomorphisms from a to the two element lattice 2 a complete lattice is called completely generated a cg lattice for short if it is generated by the set of completely prime elements or equivalently by the set of completely coprime elements then we restudy the duality between the category of t 0 alexandrov topological spaces and the category of cg lattices by means of ch a with these preparations for a frame l as the truth value table we introduce s t 0 separation axiom for stratified alexandrov l topological spaces and finally establish a duality between the category of s t 0 stratified alexandrov l topological spaces and the category of completely generated complete l ordered sets we also investigate some properties of the s t 0 axiom for example it is hereditary by closed subspaces and productive

pointwise topology on completely distributive lattices abstract in this paper the author presents a kind of pointwise topology theory on complete completely distributive lattices which is both a generalization of fuzzy topology and a further generalization of the author s papers 14 15

separation axioms in l fuzzy topological spaces i t0 and t1 abstract using the notion of remote neighborhood we define the separation axioms t 0 and t 1 in l fuzzy topological spaces l fts the relations between our definitions hutton and reilly s and wang s are discussed and the separations of hutton s fuzzy unit interval and gantner s fuzzy real line are examined characterizations of these l fts are proved and a series of properties of them are investigated moreover some results on minimal t 0 l fts and t 1 l fts are established which will be used immediately in our subsequent discussion

staged structured lotka volterra predator prey models for pest management abstract in this paper two predator prey models with stage structure are constructed and investigated in the first model continuous biological control is taken the existence and local stability of two equilibriums are studied by the liapunov stability theorem we obtain the condition for the global asymptotical stability of the trivial equilibrium i e pest eradication equilibrium in the second model impulsive biological control is taken by use of the floquet s theorem small amplitude perturbation method and comparison techniques we get the condition which guarantees the global asymptotical stability of the pest eradication periodic solution the sufficient condition for the permanence of the impulsive system is also obtained

a composite iterative algorithm for common fixed points for a finite family of nonexpansive mappings and applications this paper is concerned with a new composite iteration approximating to common fixed points for a finite family of nonexpansive mappings in banach spaces which have a uniformly gateaux differentiable norm utilizing the iterative algorithm we obtain the strong convergence theorems for a finite family of nonexpansive mappings furthermore the problem of image recovery is considered in the above result our results extend and improve the corresponding results

strong convergence theorems of modified ishikawa iterative process with errors for an infinite family of strict pseudo contractions abstract in this paper we study modified ishikawa iterative process with errors to have strong convergence for an infinite family of strict pseudo contractions in the framework of q uniformly smooth banach spaces our results improve and extend the recent ones announced by many others

continuity in quantitative domains based on the notion of an l fuzzy partially ordered set constructed in an l fuzzy approach to quantitative domain i generalized ordered set valued in frame and adjunction theory fuzzy systems and mathematics 14 2000 6 7 and by introducing the concepts of an l fuzzy directed set and the join of an l fuzzy set w r t the l fuzzy partial order l fuzzy domains are defined and the generalized scott topology on an l fuzzy domain is built this approach is similar to flagg s logic approach to quantitative domain theory a logical approach to quantitative domain theory elsevier amsterdam 1996 submitted for publication in addition the concepts of stratified approximation and a basis for an l fuzzy domain are proposed and a notion of a continuous l fuzzy domain is developed it is proved that if l is a completely distributive lattice in which 1 is irreducible and the well below relation is multiplicative then the stratified interpolation property holds in a continuous l fuzzy domain x e and ax 0 a 1 x x is a base for the generalized scott topology on x e

information systems for continuous posets abstract the method of information systems is extended from algebraic posets to continuous posets by taking a set of tokens with an ordering that is transitive and interpolative but not necessarily reflexive this develops the results of raney on completely distributive lattices and of hoofman on continuous scott domains and also generalizes smyth s r structures various constructions on continuous posets have neat descriptions in terms of these continuous information systems here we describe hoffmann lawson duality which could not be done easily with r structures and vietoris power locales we also use the method to give a partial answer to a question of johnstone s in the context of continuous posets vietoris algebras are the same as localic semilattices

a lotka volterra symbiotic model with cross diffusion abstract the main goal of this paper is to study the existence and non existence of coexistence states for a lotka volterra symbiotic model with cross diffusion we use mainly bifurcation methods and a priori bounds to give sufficient conditions in terms of the data of the problem for the existence of positive solutions we also analyze the profiles of the positive solutions when the cross diffusion parameter goes to infinity

the analysis of a finite element method for the three species lotka volterra competition diffusion with dirichlet boundary conditions a galerkin finite element method is developed for the two dimensional three dimensional nonlinear time dependent three species lotka volterra competition diffusion equations on a bounded domain the existence and uniqueness of the solution to the numerical formulation are proved an error estimate for the numerical solution is obtained numerical computations are carried out to examine the expected orders of accuracy in the error estimates

strong convergence of iterative methods by strictly pseudocontractive mappings in banach spaces abstract in this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth banach spaces first we prove that the s iteration process recently introduced by sahu in 14 converges strongly to a unique fixed point of a mapping t where t is strongly pseudocontractive mapping from a nonempty closed and convex subset c of a smooth banach space into itself it is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of i strictly pseudocontractive mappings from c into itself our results extend and improve some very recent theorems in fixed point theory and variational inequality problems particularly the results presented here extend some theorems of reich 1980 1 and yamada 2001 15 to a general class of strictly pseudocontractive mappings in uniformly smooth banach spaces

on the implicit iterative process for strictly pseudo contractive mappings in banach spaces in this paper we consider a composite implicit iterative process for an infinite family of strictly pseudo contractive mappings strong convergence theorems are established in an arbitrary real banach space the results presented in this paper improve and extend the recent ones announced by many others

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

strong convergence theorems for an infinite family of nonexpansive mappings in banach spaces in an infinite dimensional hilbert space the normal mann s iteration algorithm has only weak convergence in general even for nonexpansive mappings in order to get a strong convergence result we modify the normal mann s iterative process for an infinite family of nonexpansive mappings in the framework of banach spaces our results improve and extend the recent results announced by many others

a survey of fuzzifications of frames the papert papert isbell adjunction and sobriety this paper gives a survey of fuzzifications of frames the papert papert isbell adjunction between the categories of topological spaces and locales as well as the related concept of sobriety it then establishes categorical isomorphisms between yao l frames zhang liu l frames and l algebras lastly it studies the relationships between l sobriety modified l sobriety and i l sobriety the obtained results suggest that modified l sobriety is the most fruitful notion between the above concepts of lattice valued sobriety

the asymptotic stability of xn 1 axn bxn k 0 we obtain necessary and sufficient conditions for the asymptotic stability of the difference equation xn 1 axn bxn k 0 n 0 1 2 where the coefficients a and b are real numbers and the delay k is a nonnegative integer

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

the epireflective hull of the sierpinski object in fts abstract in the category top of topological spaces the epireflective hull of the standard two point sierpinski space is known to coincide with the subcategory of t0 topological spaces in this note we determine the epireflective hulls of the recently found sierpinski objects in the categories fts fns and top of respectively fuzzy topological spaces fuzzy neighborhood spaces and topologically generated fuzzy topological spaces we thereby identify the corresponding t0 objects in these categories and note that the categories fts fns and top are universal

generalizing homotopy analysis method to solve lotka volterra equation in the paper we generalized the homotopy analysis method to solve lotka volterra equation as a simple but typical example it illustrates the validity and the great potential of the homotopy analysis method to solve differential difference equations comparisons are made between the results of the proposed method and exact solutions the results reveal that the proposed method is valid for the lotka volterra equation

duality beyond sober spaces topological spaces and observation frames abstract we introduce observation frames as an extension of ordinary frames the aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system a full subcategory of the category of observation frames is shown to be dual to the category of t 0 topological spaces the notions we use generalize those in the adjunction between frames and topological spaces in the sense that we generalize finite meets to infinite ones we also give a predicate logic of observation frames with both infinite conjunctions and disjunctions just like there is a geometric logic for ordinary frames with infinite disjunctions but only finite conjunctions this theory is then applied to two situations firstly to upper power spaces and secondly we restrict the adjunction between the categories of topological spaces and of observation frames in order to obtain dualities for various subcategories of t 0 spaces these involve nonsober spaces

further investigations into the stability and bifurcation of a discrete predator prey model abstract in this paper we revisit a discrete predator prey model with a non monotonic functional response originally presented in hu teng and zhang 2011 6 first by citing several examples to illustrate the limitations and errors of the local stability of the equilibrium points e 3 and e 4 obtained in this article we formulate an easily verified and complete discrimination criterion for the local stability of the two equilibria here we present a very useful lemma which is a corrected version of a known result and a key tool in studying the local stability and bifurcation of an equilibrium point in a given system we then study the stability and bifurcation for the equilibrium point e 1 of this system which has not been considered in any known literature unlike known results that present a large number of mathematical formulae that are not easily verified we formulate easily verified sufficient conditions for flip bifurcation and fold bifurcation which are explicitly expressed by the coefficient of the system the center manifold theory and project method are the main tools in the analysis of bifurcations the theoretical results obtained are further illustrated by numerical simulations

convergence theorems for λ strict pseudo contractions in 2 uniformly smooth banach spaces abstract in this paper we discuss some properties of iterates generated by a strict pseudo contraction or a finite family of strict pseudo contractions in a real 2 uniformly smooth banach space the results presented in this paper are interesting extensions and improvements upon those known ones of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 324 2007 336 349 in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c this result extends a recent result of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 both from nonexpansive mappings to strict pseudo contractions and from hilbert spaces to 2 uniformly smooth banach spaces

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

iterative approaches to finding nearest common fixed points of nonexpansive mappings in hilbert spaces abstract the iteration scheme xn 1 n 1y 1 n 1 tn 1xn is first considered for infinitely many nonexpansive maps t1 t2 t3 in a hilbert space a result of shimizu and takahashi j math anal appl 211 1997 71 is generalized and it is shown that the sequence of iterates converges to py where p is some projection for this same iteration scheme with finitely many maps t1 t2 tn a complementary result to a result of bauschke j math anal appl 202 1996 150 is proved by introducing a new condition on the sequence of parameters n this condition improves lions condition c r acad sci paris ser a b 284 1977 1357 the iterates converge to py where p is the projection onto the intersection of the fixed point sets of the tis

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem