tripled coincidence theorems for contractive type mappings in partially ordered metric spaces abstract in this paper we establish tripled coincidence point theorems for a pair of mappings f x x x x and g x x satisfying a nonlinear contractive condition ordered metric spaces presented theorems extend reveral existing results in the literature v lakshmikantham l ciric coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces nonlinear anal 70 2009 4341 4349 and harjani lopez and sadarangani in article j harjani b lopez k sadarangani fixed point theorems for mixed monotone operators and applications to integral equations nonlinear anal 74 2011 1749 1760

convergence theorems best approximation and best proximity for set valued dynamic systems of relatively quasi asymptotic contractions in cone uniform spaces abstract in cone uniform spaces x using the concept of the d family of cone pseudodistances the distance between two not necessarily convex or compact sets a and b in x is defined the concepts of cyclic and noncyclic set valued dynamic systems of d relatively quasi asymptotic contractions t a b 2 a b are introduced and the best approximation and best proximity point theorems for such contractions are proved also conditions are given which guarantee that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and the limit is a best proximity point moreover d families are constructed characterized and compared the results are new for set valued and single valued dynamic systems in cone uniform cone locally convex and cone metric spaces various examples illustrating ideas methods definitions and results are constructed

fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

best proximity points for asymptotic cyclic contraction mappings abstract in this paper we prove the existence and convergence of best proximity points for asymptotic cyclic contractions in metric spaces with the property uc as well as for asymptotic proximal pointwise contractions in uniformly convex banach spaces moreover we consider a generalized cyclic contraction mapping and prove the existence of best proximity points for such a mapping in banach spaces which do not necessarily satisfy the geometric property uc

some properties of the injective tensor product of lp 0 1 and a banach space abstract let x be a real or complex banach space and 1 l p 0 1 x the injective tensor product of lp 0 1 and x has the radon nikodym property resp the analytic radon nikodym property the near radon nikodym property contains no copy of c0 is weakly sequentially complete if and only if x has the same property and each continuous linear operator from lp 0 1 to x is compact

locally convex spaces containing no copy of c0 abstract we show that locally cinvex spaces which contain no copy of c 0 have a series of very nice properties

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

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

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

some ordered fixed point results and the property p in 2010 kadelburg et al 7 by providing an example showed that a contraction in an ordered metric space is not necessarily a contraction in the classical sense thus fixed point results in ordered metric spaces are generalizations of ones in metric spaces in a sense in this paper we give some ordered fixed point results for convex contractions and special mappings which satisfy some contraction conditions also we give some results concerning the property p

boolean algebras and uniform convergence of series abstract several classical results on uniform convergence of unconditionally cauchy series are generalized to weakly unconditionally cauchy series this uniform convergence is characterized through subalgebras and subfamilies of p n a generalization of the orlicz pettis theorem is also proved by mean of subalgebras of p n

coupled fixed point theorems for contractions in fuzzy metric spaces in the present work we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

chaos synchronization and parameter identification for gyroscope system synchronization of chaos for a two degree of freedom heavy symmetric gyroscope system are studied in this paper because of the nonlinear terms of the system the system exhibits both regular and chaotic motions by lyapunov stability theory with control terms by adaptive control and by random optimization method the synchronization of two identical systems and tracking of the parameter of the systems are studied

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

on a cyclic jungck modified ts iterative procedure with application examples abstract this article investigates some convergence properties of quasi cyclic and cyclic jungck modified ts iterative schemes in complete metric spaces and banach spaces the uniqueness of the best proximity points is investigated it is basically assumed that one of the self mappings is asymptotically nonexpansive while the other is asymptotically contractive with several particular cases some application examples are also discussed

fixed point theorems for generalized contractions in ordered metric spaces abstract the purpose of this paper is to present some fixed point results for self generalized contractions in ordered metric spaces our results generalize and extend some recent results of a c m ran m c reurings a c m ran m c reurings a fixed point theorem in partially ordered sets and some applications to matrix equations proc amer math soc 132 2004 1435 1443 j j nieto r rodriguez lopez j j nieto r rodriguez lopez contractive mapping theorems in partially ordered sets and applications to ordinary differential equations order 22 2005 223 239 j j nieto r rodriguez lopez existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations acta math sin engl ser 23 2007 2205 2212 j j nieto r l pouso r rodriguez lopez j j nieto r l pouso r rodriguez lopez fixed point theorem theorems in ordered abstract sets proc amer math soc 135 2007 2505 2517 a petrusel i a rus a petrusel i a rus fixed point theorems in ordered l spaces proc amer math soc 134 2006 411 418 and r p agarwal m a el gebeily d o regan r p agarwal m a el gebeily d o regan generalized contractions in partially ordered metric spaces appl anal in press as applications existence and uniqueness results for fredholm and volterra type integral equations are given

shrinking and boundedly complete schauder frames in frechet spaces abstract we study schauder frames in frechet spaces and their duals as well as perturbation results we define shrinking and boundedly complete schauder frames on a locally convex space study the duality of these two concepts and their relation with the reflexivity of the space we characterize when an unconditional schauder frame is shrinking or boundedly complete in terms of properties of the space several examples of concrete schauder frames in function spaces are also presented

pragmatical adaptive synchronization new fuzzy model of two different and complex chaotic systems by new adaptive control abstract in this paper 1 a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and 2 a new adaptive approach and a new control lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors by using this new model the numbers of fuzzy rules of chaotic systems can be reduced from 2 n to 2 n and only 2 subsystems are needed where n is the number of nonlinear terms the fuzzy systems become much simpler in addition through the new fuzzy model the new fuzzy systems are much simpler than t s fuzzy systems when nonlinear systems are complicated and can be used to any other kind of application in fuzzy logic control or fuzzy modeling mathieu van der pol system which is called m v system in this paper and quantum cellular neural networks nanosystem which is called q cnn system in this paper are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control lyapunov function the t s fuzzy modeling and traditional adaptive control are also given in appendix b t s fuzzy model of chaotic systems appendix c traditional adaptive method for comparison

existence of the solution to variational inequality optimization problem and elliptic boundary value problem through revisited best proximity point results abstract in this paper we establish some results regarding the existence of the solution to variational inequality optimization problem and elliptic boundary value problem in hilbert spaces our strategy consists in establishing new best proximity point results in the metric spaces by introducing the concept of cyclic orbital simulative contractions we also provide nontrivial examples to show that our results are proper generalization further we improve the recent best proximity results for mappings satisfying proximal simulative conditions due to abbas et al 2017 samet 2015 and tchier et al 2016 via new class of simulation functions our results unify extend and generalize various existing results

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

weak property y0 and regularity of inductive limits abstract an inductive limit e t ind en tn is regular if and only if it satisfies the weak property y0 i e each weakly unconditionally cauchy series in e t is contained and is a weakly unconditionally cauchy series in some en tn in particular an lf space e t ind en tn is regular if and only if every weakly unconditionally cauchy series kxk is a c series i e for any scalar sequence k c0 the series k kxk is convergent furthermore for inductive limits of frechet spaces containing no copy of c0 a number of characteristic conditions of regularity are given

best proximity point theorems an exploration of a common solution to approximation and optimization problems abstract given a non self mapping t a b in the setting of a metric space this work concentrates on the resolution of the non linear programming problem of globally minimizing the real valued function x d x tx thereby yielding an optimal approximate solution to the equation tx x an iterative algorithm is also presented to compute a solution of such problems as a sequel it is possible to compute an optimal approximate solution to some non linear equations

best proximity points convergence and existence theorems for p cyclic mappings abstract we introduce a new class of mappings called p cyclic contractions which contains the p cyclic contraction mappings as a subclass then convergence and existence results of best proximity points for p cyclic contraction mappings are obtained moreover we prove results of the existence of best proximity points in a reflexive banach space these results are generalizations of the results of al thagafi and shahzad 2009 8

parameter evaluation from time sequences using chaos synchronization unknown parameters in nonlinear equations are estimated from chaotic time sequences using chaos synchronization the method is based on a random optimization method the parameters are randomly searched for in a sequential manner as the degree of the chaos synchronization is increased the method is applied for the parameter evaluation in the lorenz equation and the lang kobayashi model for the chaotic semiconductor laser

common coupled fixed point theorems in cone metric spaces for w compatible mappings in this paper we introduce the concept of a w compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non empty interior coupled common fixed point theorems for such mappings are also proved our results generalize extend and unify several well known comparable results in the literature results are supported by three examples

adaptive control in nonlinear dynamics abstract we extend an adaptive control algorithm recently suggested by huberman and lumer to multi parameter and higher dimensional nonlinear systems this control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour we find that in all cases the recovery time is linearly proportional to the inverse of control stiffness for small stiffness in higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery the control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated we further suggest methods by which periodic motion such as limit cycles can be adaptively controlled and demonstrate the robustness of the procedure in the presence of additive background noise

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 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 point theorems for weakly contractive mappings in partially ordered sets abstract the purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order

quadruple fixed point theorems for nonlinear contractions the notion of coupled fixed point is introduced by gnana bhaskar and lakshmikantham very recently the concept of tripled fixed point was introduced by berinde and borcut in this manuscript a quadruple fixed point is considered and some new related fixed point theorems are obtained we also give some examples to illustrate our results

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

a special full state hybrid projective synchronization in symmetrical chaotic systems a special full state hybrid projective synchronization type is proposed in this paper the anti synchronization and complete synchronization can be achieved simultaneously in this new synchronization phenomenon we point out how to realize this synchronization in chaotic systems anti synchronization in symmetrical coordinate subspace and complete synchronization in its normal coordinate subspace two illustrative examples multi scroll chaotic system by the partial lyapunov stability theory and a four dimensional chaotic system by the invariance principle of differential equation are presented to exhibit this new synchronization

on cyclic meir keeler contractions in metric spaces abstract cyclic meir keeler contractions are considered under the recently introduced wuc and hw properties on pairs of subsets of metric spaces we show that in contrast with previous results in the theory best proximity point theorems under these properties do not directly extend from cyclic contractions to cyclic meir keeler contractions we obtain however a positive result for cyclic meir keeler contractions under additional properties which is shown to be an extension of already existing results for cyclic contractions moreover we give examples supporting the necessity of our additional conditions

the function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems the function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized based on lyapunov stability theory and the proposed scheme the lu system and chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme

existence and uniqueness of best proximity points in geodesic metric spaces abstract a mapping t a b a b such that t a b and t b a is called a cyclic mapping a best proximity point x for such a mapping t is a point such that d x t x dist a b in this work we provide different existence and uniqueness results of best proximity points in both banach and geodesic metric spaces we improve and extend some results on this recent theory and give an affirmative partial answer to a recently posed question by eldred and veeramani in a a eldred p veeramani existence and convergence of best proximity points j math anal appl 323 2 2006 1001 1006

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

uniform convexity strong convexity and property uc abstract property uc introduced in 2009 plays a crucial role in several existence and convergence results for best proximity points and fixed points in this paper we present two approximation theoretic characterizations of uniform convexity and as consequences of these results we characterize the uniform convexity in terms of property uc characterizations of strong convexity in terms of property uc are also presented

unconditionally convergent series of operators on banach spaces abstract we show that any series n knof operators inl x y that is unconditionally convergent in the weak operator topology and satisfies the condition that n f knis a compact operator for every index setf n is unconditionally convergent in the uniform operator topology if and only ifx the dual space of the banach spacex contains no copy ofc0

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

tripled fixed point theorems for contractive type mappings in partially ordered metric spaces abstract in this paper we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence and existence and uniqueness theorems for contractive type mappings our results generalize and extend recent coupled fixed point theorems established by gnana bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 examples to support our new results are given

couple fixed point theorems for nonlinear contractions in cone metric spaces the notion of coupled fixed point is introduced by bhaskar and lakshmikantham 2006 in 13 in this manuscript some results of lakshmikantham and ciric 2009 in 5 are extended to the class of cone metric spaces

pragmatical adaptive chaos control from a new double van der pol system to a new double duffing system a new pragmatical adaptive control method for different chaotic systems is proposed traditional chaos control is limited to decrease chaos of one chaotic system this method enlarges the effective scope of chaos control we can control a chaotic system e g a new chaotic double van der pol system to a given chaotic or regular system e g a new chaotic double duffing system or to a damped simple harmonic system by a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable numerical simulations are given to show the effectiveness of the proposed scheme

a modified chua chaotic oscillator and its application to secure communications a new modification to the chua oscillator is proposed bifurcation diagrams poincare map and the lyapunov exponents are presented an application to secure communications is presented a synchronization scheme based on the modified oscillator is proposed system simulations are performed for analysis in this paper a new modified chua oscillator is introduced the original chua oscillator is well known for its simple implementation and mathematical modeling a modification of the oscillator is proposed in order to facilitate the synchronization and the encryption and decryption scheme the modification consists in changing the nonlinear term of the original oscillator to a smooth and bounded nonlinear function a bifurcation diagram a poincare map and the lyapunov exponents are presented as proofs of chaoticity of the newly modified oscillator an application to secure communications is proposed in which two channels are used numerical simulations are performed in order to analyze the communication system

asymptotically non expansive self maps and global stability with ultimate boundedness of dynamic systems this paper investigates self maps t x x which satisfy a distance constraint in a metric space with mixed point dependent non expansive properties or in particular contractive ones and potentially expansive properties related to some distance threshold the above mentioned constraint is feasible in certain real world problems of usefulness for instance when discussing ultimate boundedness in dynamic systems which guarantees lyapunov stability this fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points the results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest

common fixed point theorems in fuzzy metric spaces using the clrg property the main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces in the sense of kramosil and michalek satisfying new contractive conditions employing the common limit in the range property our results generalize and extend some recent results contained in jain et al 2012 12 to generalized contractive conditions under some control functions in the process some results about multidimensional common fixed points as coupled tripled quadrupled common fixed point results are derived from our main results

on best proximity pair theorems for relatively u continuous mappings abstract a new class of mappings called relatively u continuous is introduced and used to investigate the existence of best proximity points as an application of the existence theorem we obtain a generalized version of the markov kakutani theorem for best proximity points in the setting of a strictly convex banach space

generalized synchronization of chaotic systems by pure error dynamics and elaborate lyapunov function abstract the generalized synchronization is studied by applying pure error dynamics and elaborate lyapunov function in this paper generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation instead of current mixed error dynamics in which master state variables and slave state variables are presented the elaborate lyapunov function is applied rather than the current plain square sum lyapunov function deeply weakening the power of lyapunov direct method the scheme is successfully applied to both autonomous and nonautonomous double mathieu systems with numerical simulations

best proximity point theorems generalizing the contraction principle abstract the primary objective of this article is to elicit some interesting extensions of the simple but powerful banach s contraction principle to the case of non self mappings in fact due to the fact that best proximity point theorems fit the bill to this end the proposed extensions are presented as best proximity point theorems for non self proximal contractions which are more general than the notion of self contractions

generalized contractions in partially ordered metric spaces and applications to ordinary differential equations the purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions we also present some applications to first and second order ordinary differential equations

coupled common fixed point theorems for w compatible mappings in ordered cone metric spaces abstract we establish coupled coincidence point results for mixed g monotone mappings under general contractive conditions in partially ordered cone metric spaces over solid cones we also present results on existence and uniqueness of coupled common fixed points our results generalize extend and unify several well known comparable results in the literature to illustrate our results and to distinguish them from the earlier ones we equip the paper with examples

best proximity points for cyclic and noncyclic set valued relatively quasi asymptotic contractions in uniform spaces abstract given a uniform space x and nonempty subsets a and b of x we introduce the concepts of some families v of generalized pseudodistances on x of set valued dynamic systems of relatively quasi asymptotic contractions t a b 2 a b with respect to v and best proximity points for t in a b and we describe the methods which we use to establish the conditions guaranteeing the existence of best proximity points for t when t is cyclic i e t a 2 b and t b 2 a or when t is noncyclic i e t a 2 a and t b 2 b moreover we establish conditions guaranteeing that for each starting point each generalized sequence of iterations of these contractions in particular each dynamic process converges and the limit is a best proximity point for t in a b these best proximity points for t are determined by unique endpoints in a b for a map t 2 when t is cyclic and for a map t when t is noncyclic the results and the methods are new for set valued and single valued dynamic systems in uniform locally convex metric and banach spaces various examples illustrating the ideas of our definitions and results and fundamental differences between our results and the well known ones are given

a best proximity point theorem for weakly contractive non self mappings abstract let us consider a map t a b where a and b are two nonempty subsets of a metric space x the aim of this article is to provide sufficient conditions for the existence of a unique point x in a called the best proximity point which satisfies d x t x dist a b inf d a b a a b b our result generalizes a result due to rhoades b e rhoades some theorems on weakly contractive maps nonlinear analysis tma 47 2001 2683 2693 and hence it provides an extension of banach s contraction principle to the case of non self mappings

the existence of best proximity points in metric spaces with the property uc abstract eldred and veeramani in a a eldred p veeramani existence and convergence of best proximity points j math anal appl 323 2006 1001 1006 mr2260159 proved a theorem which ensures the existence of a best proximity point of cyclic contractions in the framework of uniformly convex banach spaces in this paper we introduce a notion of the property uc and extend the eldred and veeramani theorem to metric spaces with the property uc

coupled fixed point theorems for ϕ contractive mixed monotone mappings in partially ordered metric spaces abstract in this paper we extend the coupled fixed point theorems for mixed monotone operators f x x x obtained by bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 and luong and thuan n v luong and n x thuan coupled fixed points in partially ordered metric spaces and application nonlinear anal 74 2011 983 992 by weakening the involved contractive condition an example as well as an application to nonlinear fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations

coupled fixed point theorems for a generalized meir keeler contraction in partially ordered metric spaces abstract let x be a non empty set and f x x x be a given mapping an element x y x x is said to be a coupled fixed point of the mapping f if f x y x and f y x y in this paper we consider the case when x is a complete metric space endowed with a partial order we define generalized meir keeler type functions and we prove some coupled fixed point theorems under a generalized meir keeler contractive condition some applications of our obtained results are given the presented theorems extend and complement the recent fixed point theorems due to bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393

a note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces abstract in this paper we have used a method of reducing tripled coincidence and tripled fixed point results in ordered metric spaces to the respective results for mappings with one variable even obtaining in some cases more general theorems our results generalize extend unify enrich and complement recently tripled coincidence point theorems established by berinde and borcut 2011 4 borcut and berinde 2012 7 and borcut 2012 9 also by using our method several coupled coincidence and coupled common fixed point results in ordered metric spaces can be reduced to the coincidence and common fixed point results with one variable

coupled fixed points in partially ordered metric spaces and application abstract in this paper we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces the main results of this paper are generalizations of the main results of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 as an application we discuss the existence and uniqueness for a solution of a nonlinear integral equation

convergence and existence results for best proximity points we provide a positive answer to a question raised by eldred and veeramani a a eldred p veeramani existence and convergence of best proximity points j math anal appl 323 2006 1001 1006 about the existence of a best proximity point for a cyclic contraction map in a reflexive banach space moreover we introduce a new class of maps called cyclic contractions which contains the cyclic contraction maps as a subclass convergence and existence results of best proximity points for cyclic contraction maps are also obtained 2008 elsevier ltd all rights reserved

abscissas of weak convergence of vector valued dirichlet series abstract the abscissas of convergence uniform convergence and absolute convergence of vector valued dirichlet series with respect to the original topology and with respect to the weak topology x x of a locally convex space x in particular of a banach space x are compared the relation of their coincidence with geometric or topological properties of the underlying space x is investigated cotype in the context of banach spaces and nuclearity and certain topological invariants for frechet spaces play a relevant role

fixed point theorems in partially ordered metric spaces and applications abstract we prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order using a weak contractivity type of assumption besides including several recent developments our theorem can be used to investigate a large class of problems as an application we discuss the existence and uniqueness of solution for a periodic boundary value problem

existence and convergence of best proximity points abstract consider a self map t defined on the union of two subsets a and b of a metric space and satisfying t a b and t b a we give some contraction type existence results for a best proximity point that is a point x such that d x t x dist a b we also give an algorithm to find a best proximity point for the map t in the setting of a uniformly convex banach space

chaos synchronization of double duffing systems with parameters excited by a chaotic signal chaos synchronization by driving parameter for two uncoupled identical chaotic double duffing systems is presented replacing two corresponding parameters of the identical systems by the same function of chaotic state variables of a third chaotic system the synchronization or anti synchronization of two uncoupled systems can be obtained numerical simulations are illustrated for either synchronization or anti synchronization of which the occurrence depends significantly on initial conditions and on driving strength alternative complete synchronization and anti synchronization is also discovered

exponential synchronization of chaotic systems subject to uncertainties in the control input a sliding mode control technique is introduced for exponential synchronization of chaotic systems these systems are described by a general form including matched and unmatched nonlinear functions a new hitting free switching surface of proportional integral type is proposed this type of switching surface is without the hitting process if the attraction of sliding manifold is ensured this property makes it easy to exponentially synchronize the master slave chaotic systems based on this switching surface a robust sliding mode controller smc is derived to guarantee the attraction of sliding manifold even when the system is subjected to input uncertainties an example is included to illustrate the results developed in this paper

an extension of coupled fixed point s concept in higher dimension and applications we introduce the concept of fixed point of n order for mappings f x n x where n 2 and x is an ordered set endowed with a metric d we establish fixed point results for such mappings satisfying a given contractive condition presented theorems extend and generalize the coupled fixed point results of bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 and the tripled fixed point results of berinde and borcut v berinde m borcut tripled fixed point theorems for contractive type mappings in partially ordered metric spaces nonlinear anal 74 2011 4889 4897 some applications to integral equations and to matrix equations are also presented in this work

best proximity point theorems for cyclic orbital meir keeler contraction maps abstract we introduce a notion of cyclic orbital meir keeler contraction and give sufficient conditions for the existence of fixed points and best proximity points of such a map our main result is a generalization of a best proximity point result due to di bari et al c di bari t suzuki c vetro best proximity points for cyclic meir keeler contractions nonlinear anal 69 2008 3790 3794