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

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

the general solutions to the reflection equation of the izergin korepin model we obtain the general solutions to the reflection equation of the izergin korepin model the general solutions have two free parameters and will reduce to the non trivial diagonal solutions when both free parameters vanish it will also reduce to the solutions with upper lower triangular structures when one of the parameters vanishes moreover the hamiltonian with boundary terms for the system is obtained

knowledge spaces with graded knowledge states knowledge spaces represent a framework for assessment of knowledge with solid theoretical foundations methodology software tools and practical applications the underlying assumption in knowledge spaces is that a knowledge state of an individual is represented by a set of items which the individual has mastered in this paper we propose an extension of the theory of knowledge spaces which accounts for gradedness of knowledge states namely we assume that a knowledge state is represented by a fuzzy graded set with degrees representing levels to which an individual has mastered the items if 0 and 1 are the only degrees our approach coincides with that of ordinary knowledge spaces we develop basic concepts and results in the graded setting including bases of graded knowledge states and their computation and a logic of partial failure with its completeness theorem we also present an illustrative example the main aim of this paper is to demonstrate mathematical and computational feasibility of knowledge spaces with graded knowledge states

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

the general uq sl 2 invariant xxz integrable quantum spin chain the boundary conditions are constructed for the general xxz quantum integrable spin chain such that the resulting system is invariant under the quantum algebra uq sl 2 action the result generalizes that due to pasquier and saleur 1990 obtained for spin 1 2 and spin 1

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

isotone fuzzy galois connections with hedges we study isotone fuzzy galois connections and concept lattices parameterized by particular unary operators the operators represent linguistic hedges such as very rather more or less etc isotone fuzzy galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes we show that hedges enable us to control the number of formal concepts in the associated concept lattice we also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices

general yang baxterization of reflection equations and general k matrices of an 1 vertex models general yang baxterization of reflection equations for r with two distinct eigenvalues is presented this procedure is used to construct reflection k matrices of reflection equations for the an 1 vertex models diagonal k matrices by de vege and gonzalez ruiz 1993 for the an 1 vertex model are reproduced furthermore some new off diagonal k matrices for the an 1 vertex model are obtained

yang baxterization of reflection equations for r with two distinct eigenvalues a condition of yang baxterization of reflection equations for r with two distinct eigenvalues is given constant solutions to reflection equations for r related to fundamental representations of slq n and slq 1 1 and for r of the eight vertex model are yang baxterized

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

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

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

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

free fermionic elliptic reflection matrices and quantum group invariance diagonal solutions for the reflection matrices associated to the elliptic r matrix of the eight vertex free fermion model are presented they lead through the second derivative of the open chain transfer matrix to an xy hamiltonian in a magnetic field which is invariant under a quantum deformed clifford hopf algebra

constant solutions of reflection equations and quantum groups to the yang baxter equation an additional relation can be added this is the reflection equation that appears in various places with or without spectral parameter e g in factorizable scattering on a half line integrable lattice models with nonperiodic boundary conditions noncommutative differential geometry on quantum groups etc two forms of spectral parameter independent reflection equations are studied chosen by the requirement that their solutions be comodules with respect to the quantum group coaction leaving invariant the reflection equations for a variety of known solutions of the yang baxter equation the constant solutions of the reflection equations are given various quadratic algebras defined by the reflection equations are also given explicitly

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

boundary k matrices for the six vertex and the n 2n 1 an 1 vertex models boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices k or theta for the six vertex model the general solution depending on four arbitrary parameters is found for the an 1 models all diagonal solutions are found the associated integrable magnetic hamiltonians are explicitly derived

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

generalized coupled fixed point theorems for 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 in t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 by significantly weakening the contractive condition involved our technique of proof is essentially different and more natural an example as well as an application to periodic bvp is also given in order to illustrate the effectiveness of our generalizations

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

a coupled coincidence point result in partially ordered metric spaces for compatible mappings abstract in this paper we introduce the notion of compatibility of mappings in a partially ordered metric space and use this notion to establish a coupled coincidence point result our work extends the work 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 an example is also given

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

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

concept lattices of isotone vs antitone galois connections in graded setting mutual reducibility revisited it is well known that concept lattices of isotone and antitone galois connections induced by an ordinary binary relation and its complement are isomorphic via a natural isomorphism mapping extents to themselves and intents to their complements it is also known that in a fuzzy setting this and similar kinds of reduction fail to hold in this note we show that when the usual notion of a complement based on a residuum w r t 0 is replaced by a new one based on residua w r t arbitrary truth degrees the above mentioned reduction remains valid for ordinary relations the new and the usual complement coincide the result we present reveals a new deeper root of the reduction it is not the availability of the law of double negation but rather the fact that negations are implicitly present in the construction of concept lattices of isotone galois connections

coupled common fixed point results in two generalized metric spaces in this paper study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated these results generalize several comparable results from the current literature we also provide illustrative examples in support of our new results