a stochastic nonlinear schrodinger equation with multiplicative noise we study a conservative stochastic nonlinear schrodinger equation with a multiplicative noise we show the global existence and uniqueness of square integrable solutions for subcritical nonlinearities the critical exponent being the same in dimension 1 or 2 as the critical exponent of the deterministic equation

mass concentration phenomena for the l 2 critical nonlinear schrodinger equation in this paper we show that any solution of the nonlinear schr o dinger equation iu t delta u pm u frac 4 n u 0 which blows up in finite time satisfies a mass concentration phenomena near the blow up time our proof is essentially based on the bourgain s one cite mr99f 35184 which has established this result in the bidimensional spatial case and on a generalization of strichartz s inequality where the bidimensional spatial case was proved by moyua vargas and vega cite mr1671214 we also generalize to higher dimensions the results in keraani cite mr2216444 and merle and vega cite mr1628235

new results for studying a certain class of nonlinear delay differential systems the main aim of this technical note is to present a new approach to studying the asymptotic behavior of nonlinear delay differential systems firstly we develop a new nonlinear delay differential inequality which will be more effective and interesting than earlier ones in then we establish a new generalized barbalat s lemma which can extend and improve earlier ones in finally by combining the obtained generalized barbalat s lemma with the nonlinear delay differential inequality we obtain the attracting set and invariant set of the nonlinear delay differential systems

global well posedness and scattering for the defocusing l 2 critical nonlinear schrodinger equation when d 1 in this paper we prove global well posedness and scattering for the defocusing one dimensional mass critical nonlinear schr o dinger equation we make use of a long time strichartz estimate and a frequency localized morawetz estimate this continues work begun in earlier papers for dimensions d geq 3 and d 2

global well posedness and scattering for the energy critical nonlinear schrodinger equation in r 3 we obtain global well posedness scattering and global l 10 spacetime bounds for energy class solutions to the quintic defocusing schrodinger equa tion in r 1 3 which is energy critical in particular this establishes global existence of classical solutions our work extends the results of bourgain 4 and grillakis 20 which handled the radial case the method is similar in spirit to the induction on energy strategy of bourgain 4 but we perform the induction analysis in both frequency space and physical space simultaneously and replace the morawetz inequality by an interaction variant first used in 12 13 the principal advantage of the interaction morawetz estimate is that it is not localized to the spatial origin and so is better able to handle nonradial solutions in particular this interaction estimate together with an almost conservation argument controlling the movement of l 2 mass in fre quency space rules out the possibility of energy concentration

a barbalat like lemma with its application to learning control this paper presents the convergence property for a sequence of functions over a finite interval of time which square integral has a zero limit it is proven that if such a sequence of functions is equicontinuous the sequence itself will converge uniformly to zero over the entire interval for illustration purposes this result is applied and its usefulness shown in learning control systems analysis

best proximity points for cyclic meir keeler contractions abstract we introduce a notion of cyclic meir keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic meir keeler contractions this theorem is a generalization of a recent result due to eldred and veeramani

a remark on discontinuity at fixed point abstract in this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point r kannan 1969 9 b e rhoades 1988 14

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

equivalent contractive conditions in symmetric spaces in this paper we introduce 22 contractive conditions in symmetric spaces we prove that all these contractive conditions are equivalent then we use these conditions to get some common fixed point theorems for noncompatible maps

a variant of the meir keeler type theorem in ordered banach spaces abstract this paper discusses a projective variant of the fixed point theorem for a class of mappings satisfying the meir keeler type contraction condition in ordered banach spaces through projective metric we also prove a result on the chainability of the thompson s metric using an elementary argument

contractions of banach tarafdar meir keeler ciric jachymski matkowski and suzuki types and fixed points in uniform spaces with generalized pseudodistances in the uniform spaces sequentially complete and not sequentially complete we introduce the concept of the j families of generalized pseudodistances we apply it to construct j generalized contractions and we provide the conditions guaranteeing the existence and uniqueness of fixed points of these contractions and the convergence to these fixed points of each iterative sequence of these contractions our j generalized contractions essentially extend banach tarafdar meir keeler ciric jachymski matkowski and suzuki contractions to uniform spaces with j families of generalized pseudodistances examples showing a difference between our results and the well known ones are given the definitions the results and the method to investigate uniqueness and iterative approximation of fixed points of the maps presented here are new for maps in uniform and locally convex spaces and even in metric spaces

discussion on barbalat lemma extensions for conformable fractional integrals in this paper the barbalat type lemmas for conformable fractional order integrals which can be used to conclude the convergence of a function to zero is discussed

the uniqueness of endpoints for set valued dynamical systems of contractions of meir keeler type in uniform spaces abstract in this paper the concept of the set valued dynamical systems of contractions of meir keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established the definition and the result presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps examples show a fundamental difference between our result and the well known ones

a simple alternative to the barbalat lemma this paper gives a simple proof of the property that if a signal is square integrable and has a bounded derivative then the signal converges to zero asymptotically

a note on φ contractions in probabilistic and fuzzy metric spaces abstract in a recent paper fang 2015 1 j x fang generalized a crucial fixed point theorem for probabilistic contractions on complete menger spaces due to jachymski 2010 3 in this note we show that actually fang s theorem is an easy consequence of jachymski s theorem we also observe that the proof of a fixed point theorem for complete metric spaces deduced by fang from his main result is not correct and present a new proof of it

on the role of quadratic oscillations in nonlinear schrodinger equations ii the l 2 critical case we consider a nonlinear semi classical schrodinger equation for which quadratic oscillations lead to focusing at one point described by a nonlinear scattering operator the relevance of the nonlinearity was discussed by r carles c fermanian kammerer and i gallagher for l 2 supercritical power like nonlinearities and more general initial data the present results concern the l 2 critical case in space dimensions 1 and 2 we describe the set of non linearizable data which is larger due to the conformal invariance as an application we precise a result by f merle and l vega concerning finite time blow up for the critical schrodinger equation the proof relies on linear and nonlinear profile decompositions

new fixed point theorems for asymptotically regular multi valued maps abstract recently extending ciric s quasi contraction to a very general setting proinov petko d proinov fixed point theorems in metric spaces nonlinear anal 64 2006 546 557 obtained a remarkable fixed point theorem we utilize proinov s contractive type hypotheses for a self map of a metric space to obtain very general fixed point theorems for multi valued maps in metric spaces

equivalent conditions for generalized contractions on ordered metric spaces abstract we establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane as its application we get that various contractive conditions using the so called altering distance functions coincide with classical ones we consider several classes of mappings both on metric spaces and ordered metric spaces in particular we show that unexpectedly some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by harjani and sadarangani j harjani k sadarangani generalized contractions in partially ordered metric spaces and applications to ordinary differential equations nonlinear anal 72 2010 1188 1197 and amini harandi and emami a amini harandi h emami a fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations nonlinear anal 72 2010 2238 2242 do follow from an earlier result of o regan and petrusel d o regan and a petrusel fixed point theorems for generalized contractions in ordered metric spaces j math anal appl 341 2008 1241 1252

a generalization of the banach contraction principle with high order of convergence of successive approximations in this paper we present the following generalization of the banach contraction principle let t d x xt d x x be a continuous operator on a complete metric space x d x d satisfying d tx t2x d x tx for all x d tx d with d x tx j where j r j r is an interval containing 0 j j j j is a gauge function of order r 1r 1 on jj in the sense that 0 0 t tr 0 0 t tr is nondecreasing on j 0 j 0 and t t t t on j 0 j 0 suppose that x0 dx0 d is an initial point such that d x0 tx0 jd x0 tx0 j and all of the iterates xn 1 txn n 0 1 belong to dd then the iterative sequence xn 1 txnxn 1 txn converges to a fixed point of tt with error estimates d xn sn r 1 rnd x0 tx0 andd xn d xn xn 1 1 d xn xn 1 where sn r 1 r rn 1 d x0 tx0 sn r 1 r rn 1 d x0 tx0 and is a nonnegative and nondecreasing function on jj such that t t t this fixed point theorem includes as special cases some results of mysovskih i p mysovskih on the convergence of l v kantorovic s method of solution of functional equations and its applications dokl acad nauk sssr 70 1950 565 568 in russian rheinboldt w c rheinboldt a unified convergence theory for a class of iterative processes siam j numer anal 5 1968 42 63 gel man a gel man a certain fixed point principle dokl akad nauk sssr 198 1971 506 508 in russian soviet math dokl 12 1971 813 816 engl transl huang z d huang on newton s method under holder continuous derivative j math anal appl 270 2002 332 339 and others

subcritical approximations to stochastic defocusing mass critical nonlinear schrodinger equation on r abstract we show robustness of various truncated and subcritical approximations to the stochastic defocusing mass critical nonlinear schrodinger equation nls in dimension d 1 whose solution was constructed in 8 with one particular such approximation the key ingredient in the proof is a uniform bound of the solutions to the family of deterministic mass subcritical defocusing nls

fixed point theorems in metric spaces abstract in this paper we establish two general theorems for equivalence between the meir keeler type contractive conditions and the contractive definitions involving gauge functions one of these theorems is an extension of a recent result of lim on characterization of meir keeler contractive maps nonlinear anal 46 2001 113 120 also we establish the following new fixed point theorem suppose r r is a contractive gauge function in the sense that for any e 0 there exists e such that e t implies t e and suppose t is a continuous and asymptotically regular selfmapping on a complete metric space x d satisfying the following i d tx ty d x y for all x y x and ii d tx ty d x y for all x y x with x y where d x y d x y d x tx d y ty with 0 then t has a unique fixed point and all of the picard iterates of t converge to this fixed point this result includes those of jachimski equivalent conditions and the meir keeler type theorems j math anal appl 194 1995 293 303 matkowski fixed point theorems for contractive mappings in metric spaces cas pest mat 105 1980 341 344 and others

optimal bilinear control of stochastic nonlinear schrodinger equations mass sub critical case we study optimal control problems for stochastic nonlinear schrodinger equations in both the mass subcritical and critical case for general initial data of the minimal l 2 regularity we prove the existence and first order lagrange condition of an open loop control in particular these results apply to the stochastic nonlinear schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two respectively furthermore we obtain uniform estimates of backward stochastic solutions in new spaces of type u 2 and v 2 adapted to evolution operators related to linear schrodinger equations with lower order perturbations these estimates yield a new temporal regularity of backward stochastic solutions which is crucial for the tightness of approximating controls induced by ekeland s variational principle

generalized meir keeler type contractions on g metric spaces in this manuscript we introduce generalized meir keeler type contractions over g metric spaces moreover we show that every orbitally continuous generalized meir keeler type contraction has a unique fixed point on complete g metric spaces we illustrate our results by some given examples

some φ coupled fixed point results via modified f control function s concept in metric spaces and its applications abstract the aim of this paper is to propose a new coupled fixed point theorem for a mixed monotone mapping in a metric space which is taken no account of the continuity of the mapping to this end we introduce the notions of coupled fixed point and modified f control function our obtained results are applied to derive some coupled fixed point theorems in partial metric spaces and quasi metric spaces respectively some applications to matrix equations and integral equations are also presented so as to illustrate our results

endpoints of set valued dynamical systems of asymptotic contractions of meir keeler type and strict contractions in uniform spaces abstract in this paper we introduce the concepts of the set valued dynamical systems of asymptotic contractions of meir keeler type and set valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions the result concerning the investigations of problems of the set valued asymptotic fixed point theory include some well known results of meir and keeler kirk and suzuki concerning the asymptotic fixed point theory of single valued maps in metric spaces the result concerning set valued strict contractions in which the contractive coefficient is not constant is different from the result of yuan concerning the existence of endpoints of tarafdar vyborny generalized contractions in which the contractive coefficient is constant in bounded metric spaces and provides some examples of tarafdar yuan topological contractions in compact uniform spaces definitions and results presented here are new for set valued dynamical systems in uniform locally convex and metric spaces and even for single valued maps examples show a fundamental difference between our results and the well known ones

fixed points for generalized contractions and applications to control theory the concepts of weak strong topological contraction and a generalization of banach contraction mappings called p contraction are introduced and used to prove fixed point theorems for self mappings from a topological metric space into itself satisfying topological contraction metric p contraction respectively certain non linear integral equations defined on c a b satisfying generalized lipschitzian conditions can easily be solved by applying these theorems in the sequel we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming

remarks on contractive conditions of integral type abstract we show that most contractive conditions of integral type given recently by many authors coincide with classical ones this is done with the help of a geometric lemma on subsets of the quadrant 0 2 in particular we extend a recent result of suzuki who observed that an integral version of the banach contraction principle given by branciari could be derived from a classical fixed point theorem of meir and keeler nevertheless we also give a new contractive condition of integral type which is independent of classical ones since it does not force the nonexpansiveness of a mapping

on park s open questions and some fixed point theorems for general contractive type mappings in this paper we answer two fixed point questions of park by constructing ten nontrivial examples and prove some fixed point theorems for general contractive type mappings which in turn generalize improve and unify some results due to fisher hegedus hegedus and szilagyi hikida kasahara park park and rhoades and others