partially ordered cone metric spaces and coupled fixed point results bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 studied the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x e karapinar e karapinar couple fixed point theorems for nonlinear contractions in cone metric spaces comput math appl 2010 doi 10 1016 j camwa 2010 03 062 proved some results of the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x over normal cones without regularity in the present paper we prove that coupled coincidence fixed point theorems over cone metric spaces are not necessarily normal our results generalize several well known comparable results in the literature

one dimensional asymptotic classes of finite structures a collection c of finite l structures is a 1 dimensional asymptotic class if for every m n and every formula x y where y y 1 y m i there is a positive constant c and a finite set e c r 0 such that for every m c and a m m either m a c or for some e m a m c m 1 2 ii for every e there is an l formula y such that m m is precisely the set of a m m with m a m c m 1 2 one dimensional asymptotic classes are introduced and studied here these classes come equipped with a notion of dimension that is intended to provide for the study of classes of finite structures a concept that is central in the development of model theory for infinite structures connections with the model theory of infinite structures are also drawn

coupled fixed point results for ψ φ weakly contractive mappings in ordered g metric spaces in this paper we establish coupled coincidence and common coupled fixed point theorems for j f weakly contractive mappings in ordered g metric spaces presented theorems extend generalize and improve many existing results in the literature an example is given

coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces coupled fixed point problems have attracted much attention in recent times in this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces the two mappings considered here are assumed to be compatible hadzic type t norm is used by an application of the coincidence point theorem in fuzzy metric spaces a corresponding result is obtained in metric spaces the main theorem of this paper is illustrated with an example our work extends some existing results

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

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

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

affine covers of lie geometries and the amalgamation property certain classes of smoothly approximable structures the class of affine covers of lie geometries are shown to have the amalgamation property in particular this shows that any affine cover of a lie geometry has the small index property 2000 mathematical subject classification 03c45

absence of wandering domains for some real entire functions with bounded singular sets let f be a real entire function whose set s f of singular values is real and bounded we show that if f satisfies a certain function theoretic condition the sector condition then f has no wandering domains our result includes all maps of the form z mapsto lambda frac sinh z z a with lambda 0 and a in mathbb r we also show the absence of wandering domains for certain non real entire functions for which s f is bounded and f n s f rightarrow infty uniformly as a special case of our theorem we give a short elementary and non technical proof that the julia set of the exponential map f z e z is the entire complex plane furthermore we apply similar methods to extend a result of bergweiler concerning baker domains of entire functions and their relation to the postsingular set to the case of meromorphic functions

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

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

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

normality and repelling periodic points let k 3 2 be an integer and f be a family of functions meromorphic in a domain d c c all of whose poles have multiplicity at least 2 at least 3 if in d each f f has neither repelling fixed points nor repelling periodic points of period k then f is a normal family in d examples are given to show that the conditions on poles are necessary and sharp

on the connectivity of the julia sets of meromorphic functions we prove that every transcendental meromorphic map f with disconnected julia set has a weakly repelling fixed point this implies that the julia set of newton s method for finding zeroes of an entire map is connected moreover extending a result of cowen for holomorphic self maps of the disc we show the existence of absorbing domains for holomorphic self maps of hyperbolic regions whose iterates tend to a boundary point in particular the results imply that periodic baker domains of newton s method for entire maps are simply connected which solves a well known open question

fixed point theorems in partially ordered metric spaces for operators with ppf dependence abstract in this paper fixed point theorems of a nonlinear operator are developed where the domain space c a b e is different from the range e which is a metric space with partial order an application of the fixed point theorem to a periodic boundary value problem with delay is also given

hyperbolic entire functions and the eremenko lyubich class class mathcal b or not class mathcal b hyperbolicity plays an important role in the study of dynamical systems and is a key concept in the iteration of rational functions of one complex variable hyperbolic systems have also been considered in the study of transcendental entire functions there does not appear to be an agreed definition of the concept in this context due to complications arising from the non compactness of the phase space in this article we consider a natural definition of hyperbolicity that requires expanding properties on the preimage of a punctured neighbourhood of the isolated singularity we show that this definition is equivalent to another commonly used one a transcendental entire function is hyperbolic if and only if its postsingular set is a compact subset of the fatou set this leads us to propose that this notion should be used as the general definition of hyperbolicity in the context of entire functions and in particular that speaking about hyperbolicity makes sense only within the eremenko lyubich class mathcal b of transcendental entire functions with a bounded set of singular values we also considerably strengthen a recent characterisation of the class mathcal b by showing that functions outside of this class cannot be expanding with respect to a metric whose density decays at most polynomially in particular this implies that no transcendental entire function can be expanding with respect to the spherical metric finally we give a characterisation of an analogous class of functions analytic in a hyperbolic domain

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

wandering domains in the iteration of entire functions fonctions entieres a domaines multiplement connexes de normalite ensembles de fatou julia pour des fonctions qui commuttent exemples de type d herman classes de fonctions entieres sans domaines d errance

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

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

are there critical points on the boundaries of singular domains generalizing a result of e ghys we prove a general theorem that implies that if a rational functionf of the riemann sphere of degree 2 leaves invariant a singular domainc a disk or a ring on which the rotation number off satisfies a diophantine condition provided that on bar c f is injective then each boundary component ofc contains critical point off the injectivity condition is always satisfied for singular disks associated to linearizable periodic elliptic points off z z n a withne n 2 andae we also show that the singular disks associated to periodic elliptic points off z e az that satisfy a diophantine condition are unbounded in in the end of the paper we give a survey of the theory of iteration of entire functions of

automorphisms of chevalley groups of different types over commutative rings abstract in this paper we prove that every automorphism of elementary adjoint chevalley group with root system of rank 1 over a commutative ring with 1 2 for the systems a 2 f 4 b l c l with 1 2 and 1 3 for the system g 2 is standard i e it is a composition of ring inner central and graph automorphisms

automorphisms of chevalley groups of type f4 over local rings with 1 2 abstract in the given paper we prove that every automorphism of a chevalley group of type f 4 over a commutative local ring with 1 2 is standard i e it is a composition of ring and inner automorphisms

accesses to infinity from fatou components we study the boundary behaviour of a meromorphic map f c c on its invariant simply connected fatou component u to this aim we develop the theory of accesses to boundary points of u and their relation to the dynamics of f in particular we establish a correspondence between invariant accesses from u to infinity or weakly repelling points of f and boundary fixed points of the associated inner function on the unit disc we apply our results to describe the accesses to infinity from invariant fatou components of the newton maps

multiply connected wandering domains of entire functions the dynamical behaviour of a transcendental entire function in any periodic component of the fatou set is well understood here we study the dynamical behaviour of a transcendental entire function f in any multiply connected wandering domain u of f by introducing a certain positive harmonic function h in u related to harmonic measure we are able to give the first detailed description of this dynamical behaviour using this new technique we show that for sufficiently large n the image domains u n f n u contain large annuli c n and that the union of these annuli acts as an absorbing set for the iterates of f in u moreover f behaves like a monomial within each of these annuli and the orbits of points in u settle in the long term at particular levels within the annuli determined by the function h we also discuss the proximity of partial u n and partial c n for large n and the connectivity properties of the components of u n setminus overline c n these properties are deduced from new results about the behaviour of entire functions that omit certain values in an annulus

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

on the fatou components of two permutable transcendental entire functions abstract let f and g be two distinct permutable transcendental entire functions suppose further that q g aq f b for some nonconstant polynomial q z and constants a 0 b c in this article we will investigate the dynamical properties of f and g and show that they have the same fatou sets with the same components

a fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations we present a fixed point theorem for generalized contraction in partially ordered complete metric spaces as an application we give an existence and uniqueness for the solution of a periodic boundary value problem

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

coupled fixed point results for ψ φ weakly contractive condition in ordered partial metric spaces in this paper we prove some coupled fixed point theorems involving a j f weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces these results are analogous to theorems of van luong and xuan thuan 2011 10 on the class of ordered partial metric spaces also an application is given to support our results

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

envelopes of holomorphy and holomorphic discs the envelope of holomorphy of an arbitrary domain in a two dimensional stein manifold is identified with a connected component of the set of equivalence classes of analytic discs immersed into the stein manifold with boundary in the domain this implies in particular that for each of its points the envelope of holomorphy contains an embedded non singular riemann surface and also an immersed analytic disc passing through this point with boundary contained in the natural embedding of the original domain into its envelope of holomorphy moreover it says that analytic continuation to a neighbourhood of an arbitrary point of the envelope of holomorphy can be performed by applying the continuity principle once another corollary concerns representation of certain elements of the fundamental group of the domain by boundaries of analytic discs a particular case is the following given a contact three manifold with stein filling any element of the fundamental group of the contact manifold whose representatives are contractible in the filling can be represented by the boundary of an immersed analytic disc