initial value problems for the second order mixed monotone type of impulsive differential equations in banach spaces in this paper we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence and uniqueness theorem of solutions of initial value problems for the second order mixed monotone type of impulsive differential equations and its application

existence of a positive almost periodic solution for a nonlinear delay integral equation in this paper we discuss the existence of positive almost periodic solution for some nonlinear delay integral equation by constructing a new fixed point theorem in the cone some known results are extended

thompson s metric and mixed monotone operators abstract we apply thompson s metric to prove several fixed point theorems of mixed monotone operators by appealing to various generalizations of banach s fixed point theorem

high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

the method of mixed monotony and first order differential systems on considere des problemes aux valeurs initiales et aux valeurs limites periodiques pour des equations differentielles d ordre 1 on developpe la methode de monotonie mixte pour etudier la construction de suites monotones qui converge vers la solution unique

existence and uniqueness of fixed points for some mixed monotone operators abstract in this paper we introduce the e concave convex operator without any compact or continuous assumptions we prove the existence and uniqueness of fixed points giving monotone iterative sequences for the unique fixed point for the operator finally we apply the results to an integral equation of polynomial type which possesses items of measurable functions

subsets of the square with the continuous and order preserving fixed point property abstract this study characterizes the convex sets whose complements in the unit square exhibit the fixed point property for mappings which are jointly continuous and order preserving hence one can readily construct simple sets with this fixed point property but which neither have the fixed point property individually for continuous mappings nor for order preserving mappings this is the first characterization of any non trivial set with this property

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

existence of coupled quasi fixed points for mixed monotone operators and its application to the discontinuous integral equations existence theorems of minimal and maximal coupled quasi fixed points for the complex type mixed monotone operator in partial order topological spaces are established as its application we investigate the existence of the minimal and maximal coupled quasi solution for the discontinuous hammerstein integral equation in banach space our results improve and extend some well known results

existence and uniqueness of fixed points for mixed monotone operators with applications in this paper we study the uniqueness and existence of fixed points of mixed monotone operators in the partially ordered banach space our conclusions essentially improve the relevant results obtained by liang and others moreover as an application of our results we prove the existence and uniqueness of a positive solution for a class of integral equations which cannot be solved by using previously available methods

new fixed point theorems and applications of mixed monotone operator in this paper we study the uniqueness and existence of fixed point of mixed monotone operators in the partially ordered banach space the results extend and improve recent related results

output regulation of nonlinear systems with nonhyperbolic zero dynamics previous solvability conditions for the output relation of nonlinear systems are applicable only to those with hyperbolic zero dynamics it is shown in this note that output regulation of nonlinear systems with nonhyperbolic zero dynamics is also possible by a reduction of the plant dynamics and an augmentation of the exosystem

multidimensional fixed point theorems in partially ordered complete metric spaces abstract in this paper we propose a notion of coincidence point between mappings in any number of variables and we prove some existence and uniqueness fixed point theorems for nonlinear mappings verifying different kinds of contractive conditions and defined on partially ordered metric spaces these theorems extend and clarify very recent results that can be found in t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 v berinde m borcut tripled fixed point theorems for contractive type mappings in partially ordered metric spaces nonlinear anal 74 2011 4889 4897 and m berzig b samet an extension of coupled fixed point s concept in higher dimension and applications comput math appl 63 8 2012 1319 1334

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

second order functional differential equations with past present and future dependence abstract in this paper we obtain a result on existence of extremal quasisolutions and solutions for second order functional differential equations with functional boundary conditions and past present and future dependence in order to do that we develop a generalized monotone method in presence of lower and upper solutions some examples of application are provided too

on solvability of functional equations and system of functional equations arising in dynamic programming the purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes by using fixed point theorems a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established under certain conditions some existence theorems of coincidence solutions for the class of system of functional equations are shown some examples are given to demonstrate the advantage of our results than existing ones in the literature

error estimates for approximation of coupled best proximity points for cyclic contractive maps we enrich the known results about coupled fixed and best proximity points of cyclic contraction ordered pair of maps the uniqueness of the coupled best proximity points for cyclic contraction ordered pair of maps in a uniformly convex banach space is proven we find a priori and a posteriori error estimates for the coupled best proximity points obtained by sequences of successive iterations when the underlying banach space has modulus of convexity of power type a looser conditions are presented for the existence and uniqueness of coupled fixed points of a cyclic contraction ordered pair of maps in a complete metric space and a priori a posteriori error estimates and the rate of convergence for the coupled fixed points are obtained for the sequences of successive iterations we apply these results for solving systems of integral equations systems of linear and nonlinear equations

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

new existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation abstract in this paper we obtain some new and general existence and uniqueness theorems of positive fixed points for mixed monotone operators with perturbation which extend the corresponding results in z t zhang new fixed point theorems of mixed monotone operators and applications j math anal appl 204 1996 307 319 theorem 1 corollaries 1 and 2 moreover some applications to nonlinear integral equations on unbounded region are given

fixed points of discontinuous multivalued increasing operators in banach spaces with applications by using relatively weakly compactness conditions we obtain existence theorems of fixed points for discontinuous multivalued increasing operators in banach spaces as an application we utilize the results obtained in section 2 to lead to the existence principles for integral inclusions of hammerstein type multivalued maps

the principle and models of dynamic programming v in this article we introduce two new concepts namely dynamic geometry and dynamic pattern the former can be further developed in conjunction with computer graphics while the latter can be further developed in conjunction with the concept of dp in the sense of zelkowitz et al

on fixed point theorems of mixed monotone operators and applications abstract in this paper we obtain some new existence and uniqueness theorems of positive fixed point of mixed monotone operators in banach spaces partially ordered by a cone finally we apply the main theorem to a nonlinear parabolic partial differential equation some results are new even for increasing or decreasing operators

representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs an algorithm is presented for transforming a nonlinear state space system into a threefold set of equations the first subset describing the dynamics of the unobservable part of the system the second subset representing the remaining state variables as functions of inputs and outputs and their derivatives and the last subset defining the external behaviour of the system

viscosity solutions of fully nonlinear parabolic systems abstract in this paper we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their cauchy dirichlet problem we prove the existence uniqueness and continuity of viscosity solution by combining perron s method with the technique of coupled solutions the results here generalize those in proc london math soc 63 1991 212 240 and comm partial differential equations 16 1991 1095 1128

computational aspects of the coarsening at random model and the shapley value this paper is concerned with computational aspects of coarse data in information technology a method for calculating the car coarsening at random model of a finite random set is obtained and a formula for computing the shapley value using the distribution of the random set is given the relationship between the car model solution and the shapley value is also discussed several examples are given to illustrate our results

multidimensional fixed point theorems under ψ φ contractive conditions in partially ordered complete metric spaces in this paper we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak contractive condition our results generalize extend and unify several classical and very recent related results in the literature see aydi et al 2011 berinde 2010 gnana bhaskar and lakshmikantham 2006 berzig and samet 2012 borcut and berinde 2012 choudhury et al 2011 karapinar and luong 2012 lakshmikantham and iric 2009 luong and thuan 2011 roldan 2012

fixed point results for mappings satisfying ψ φ weakly contractive condition in partially ordered metric spaces abstract we establish coincidence fixed point and common fixed point theorems for mappings satisfying weakly contractive condition in an ordered complete metric space some applications of our obtained results are given

fixed point theorems for mixed monotone operators and applications to integral equations abstract the purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions we also present an application to integral equations

fixed points for mixed monotone multivalued operators in banach spaces with applications abstract in this paper the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed we present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition we also give some applications to differential inclusions with discontinuous right hand side in banach spaces and to hammerstein integral inclusions on r n

multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces in recent times coupled tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions roldan et al showed a unified version of these results for nonlinear mappings in any number of variables which were not necessarily permuted or ordered introducing the notion of multidimensional coincidence point very recently choudhury et al proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of george and veeramani in this paper using the idea of coincidence point for nonlinear mappings in any number of variables we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with hadzic type t norms then we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied

almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance affected unstable zero dynamics the problem of global almost disturbance decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by disturbance this result complements some recent work on the topic where unstable zero dynamics is not allowed to be affected by the disturbances

coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces abstract the purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces we also present a result on the existence and uniqueness of coupled common fixed points an example is given to support the usability of our results

controlled invariance for nonlinear systems necessary and sufficient conditions are derived for a b invariance called here controlled invariance for nonlinear systems dot x f x u the obtained results generalize and elucidate already known results about systems dot x a x sum min i 1 max m u i b i x a new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

existence theorems of solutions for certain classes of functional equations arising in dynamic programming in this paper we study the existence uniqueness and iterative approximation of solutions for certain classes of functional equations arising in dynamic programming of multistage decision processes the results presented here generalize improve and unify the corresponding results of other authors

the omega limit sets of ray contractive operators abstract in this paper we study the omega limit sets of a ray contractive map t without the compactness assumption on the orbits if there exists a compact subset of k the interior of a closed convex cone k such that t and t k 0 k then we are able to prove that x either consists of a single point or forms a cycle 2 periodic orbit for any x k

the analysis of zero dynamics of nonlinear control systems with symmetries zero dynamics of nonlinear control systems with symmetries are studied in this paper it is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition a local zero dynamics is always possible to be extended to the semiglobal case the relation between the zero dynamics and the quotient system is also discussed

fixed point theorems for generalized contractions in partially ordered metric spaces with semi monotone metric abstract in this paper we study the existence and uniqueness of coupled fixed points for mixed monotone mappings in partially ordered metric spaces with semi monotone metric as an application we prove the existence and uniqueness of the solution for a first order differential equation with periodic boundary conditions

fixed point theorems of φ concave ψ convex mixed monotone operators and applications abstract in this paper concave convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained moreover some applications to nonlinear integral equations on bounded or unbounded regions are given

positive almost periodic solutions of some neutral integral equation abstract in this paper we investigate the existence of positive almost periodic solutions for some neutral integral equation by constructing a new fixed point theorem in the cone some new results are obtained

global robust stabilization of minimum phase nonlinear systems with uncertainty the problem of global stabilization via state feedback is studied for a class of minimum phase nonlinear systems with unknown unmodelled time varying parameters or disturbances belonging to a given compact set sufficient conditions are presented for the existence of a robust stabilizing state feedback controller the controller is constructed explicitly by using a lyapunov based recursive design procedure the proposed feedback control law is a smooth function of the state and requires information of bounding functions on the size of uncertainties in the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system an adaptive controller is developed based on similar arguments achieving global stability with state regulation the main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics

coupled fixed points of nonlinear operators with applications a partir de quasi solutions couplees des problemes aux valeurs initiales pour des equations differentielles ordinaires on introuit le concept de points fixes couples abstraits pour certains operateurs on donne des theoremes d existence

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

coupled fixed points of multivalued operators and first order odes with state dependent deviating arguments abstract we establish a coupled fixed point theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on the existence of quasisolutions and unique solutions to first order functional differential equations with state dependent deviating arguments our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments but we emphasize that they are new even for differential equations with continuously state dependent delays

new fixed point theorems of mixed monotone operators and applications in this paper a class of mixed monotone operators with convexity and concavity are investigated and existence and uniqueness theorems of fixed points are obtained moreover some applications to nonlinear integral equations on unbounded regions and differential equations in banach spaces are given

iterative method for coupled quasi solutions of mixed monotone operator equations in this paper we obtain some new existence theorems of the coupled quasi fixed points for mixed monotone operators under more general conditions our results improve and extend many well known results finally we apply our results to hammerstein integral equations

second order singular boundary value problems with integral boundary conditions abstract we study the second order singular boundary value problem u f t u 0 t 0 1 u 0 0 1 u s d s u 1 0 1 u s d s sufficient conditions are obtained for the existence and uniqueness of positive solutions the dependence of positive solutions on the parameter is also studied moreover application of our theory to a special problem is discussed to prove our theorem we utilize some results from the mixed monotone operator theory

iterative method for solutions and coupled quasi solutions of nonlinear integro differential equations of mixed type in banach spaces we consider in this paper the existence of solutions coupled minimal and maximal quasi solutions and iterative approximation of the unique solution for the following initial value problems ivp of the nonlinear integro di erential equations of mixed type in ordered banach spaces e u f t u u tu su t i u t0 x0 1 where i t0 t0 a a 0 x0 e f c i e e e e e and

stabilization of nonlinear systems via designed center manifold this paper addresses the problem of local state feedback stabilization of a class of nonlinear systems with nonminimum phase zero dynamics a new technique namely the lyapunov function with homogeneous derivative along solution curves was developed to test the approximate stability of the dynamics on the center manifold a set of convenient sufficient conditions are provided to test the negativity of the homogeneous derivatives using these conditions and assuming the zero dynamics has stable and center linear parts a method is proposed to design controls such that the dynamics on the designed center manifold of the closed loop system is approximately stable it is proved that using this method the first variables in each of the integral chains of the linearized part of the system do not affect the approximation order of the dynamics on the center manifold based on this fact the concept of injection degree is proposed according to different kinds of injection degrees certain sufficient conditions are obtained for the stabilizability of the nonminimum phase zero dynamics corresponding formulas are presented for the design of controls

interaction transform of set functions over a finite set the paper introduces a new transform of set functions over a finite set which is linear and invertible as the well known mobius transform in combinatorics this transform leads to the interaction index a central concept in multicriteria decision making the interaction index of a singleton happens to be the shapley value of the set function or in terms of cooperative game theory of the value function of the game properties of this new transform are studied in detail and some illustrative examples are given

bhaskar guo lakshmikantam ciric type results via new functions with applications to integral equations abstract in this paper by using the c class functions we present some coupled coincidence point results for a pair of mappings satisfying generalized weakly contractive condition in the context of ordered b metric spaces also an application to study the existence of solutions for the nonlinear integral equations and example are given to support our theoretical results

bounded tracking for non minimum phase nonlinear systems with fast zero dynamics in this paper we derive tracking control laws for non minimum phase nonlinear systems with both fast and slow possibly unstable zero dynamics the fast zero dynamics arise from a perturbation of a nominal system these fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs in this paper we combine the ideas from some recent work of hunt meyer and su with that of devasia chen and paden on an asymptotic tracking procedure for non minimum phase nonlinear systems we give somewhat subtle conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero explicit bounds on the control inputs are calculated for both siso and mimo systems using some interesting non standard singular perturbation techniques the method is applied to a suite of examples including the simplified planar dynamics of vtol and ctol aircraft

some new results concerning random sets and fuzzy sets abstract this paper is a continuation of past work showing direct connections between fuzzy set theory and classical probability theory through the use of random sets this includes characterizations of random intervals one point coverage equivalent to fuzzy sets determination of all nested random sets equivalent to fuzzy sets the solution of the one and multiple point coverage problems for random sets in finite spaces and the use of entropy for ordering random sets within the class of one point coverage equivalent ones for any given fuzzy set finally a connection between random variables random sets and fuzzy sets is pointed out

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

existence theorems of coupled fixed points abstract by associating with a mixed monotone operator a monotone operator on product space several existence theorems of coupled fixed points are proved

on modeling of linguistic information using random sets this paper discusses the formal connection between possibility distributions zadeh 21 and the theory of random sets via choquet s theorem based upon these relationships it is suggested that plausible inferences and modeling of common sense can be derived from the statistics of random sets the analysis of subjectivity in meaning representation of natural languages can be carried out by taking account of covariates of individuals as in the statistical analysis of survival data

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

fixed point theorems for a class of mixed monotone operators with applications abstract in this paper we provide several unique existence theorems for fixed points for mixed monotone operators without continuity and compactness and apply them to study a class of integral equations

mixed monotone iterative technique for a class of semilinear impulsive evolution equations in banach spaces abstract this paper deals with the existence of mild l quasi solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered banach space e under a new concept of upper and lower solutions a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established the results improve and extend some relevant results in ordinary differential equations and partial differential equations an example is also given

fixed point theorems of ϕ convex ψ concave mixed monotone operators and applications in this paper convex concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained as an application we give one example to illustrate our results

solution of a class of nonlinear matrix equations abstract in this paper we solve nonlinear matrix equations of the form x q i 1 p a i f i x a i r i and x q i 1 p a i f i x a i r i j 1 q b j g j x b j q j where 1 1 r i q j 1 1 q p n the collection of all n n hermitian positive definite matrices and a i b j s are n n matrices also f i g j s are monotone mappings from p n into p n examples are given to illustrate that the equations can not be solved by previously known theorems

stabilization via dynamic output feedback for systems with output nonlinearities abstract the problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered these systems are characterized by nonlinear terms depending only on the ouputs it is shown that for these systems stabilization via continuous state feedback plus stabilization via output injection imply stabilization via continuous dynamic output feedback this generalizes a well knwon result for linear systems

minimum phase properties for input nonaffine nonlinear systems for input nonaffine nonlinear control systems the minimum phase property of the system in general depends on the control law switching or discontinuous controllers may offer advantages in this context in particular there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are locally stable whereas a discontinuous controller which achieves this exists for single input single output input nonaffine nonlinear systems we give sufficient conditions for existence and present a method for the design of discontinuous switching controllers which yield locally stable zero dynamics

on static output feedback stabilization of systems with stable generalized zero dynamics in this note we define generalized zero dynamics introduce a generalized zero dynamics algorithm and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback

gaussian processes and martingales for fuzzy valued random variables with continuous parameter abstract the purpose of this paper is to discuss fuzzy valued gaussian processes and martingales with continuous parameter we mainly obtain a representation theorem for fuzzy valued gaussian processes after proving a new embedding theorem based on previous results about set valued and fuzzy valued martingales cf s li y ogura j fuzzy math 4 1996 905 s li y ogura fuzzy sets and systems 101 1999 453 s li y ogura ann probab 26 1998 1384 1402 s li y ogura in proc ifsa 97 vol 4 1997 pp 9 13 s li y ogura in c bertoluzza m a gil d a ralescu eds statistical modeling analysis and management of fuzzy data physica in press y ogura s li fuzzy sets and systems in press we prove optional sampling theorems for set valued and fuzzy valued martingales with continuous parameter

on some coupled quasi fixed points theorems abstract some existence theorems are known for coupled quasi fixed points of nonlinear mixed monotone operators from a k fold conical segment u 0 v 0 into a real banach space where k 1 or 2 in this note we extend those results to an arbitrary but finite k by a simple but nontrivial iterative mechanism interestingly enough for mixed monotone operators with k 3 folds the lipschitz condition ensuring the uniqueness of their fixed points is as simple as the cases of k 2