from quasivariational inclusion problems to stampacchia vector quasiequilibrium problems stampacchia set valued vector ekeland s variational principle and caristi s fixed point theorem abstract in this paper we first study existence theorems of solution for quasivariational inclusion problems we apply existence theorems of solution for quasivariational inclusion problem to study the existence theorems of solution for the stampacchia generalized vector quasiequilibrium problems and stampacchia vector quasiequilibrium problems our results and approach to the stampacchia generalized vector quasiequilibrium problem are different from any existence results of this type of problem finally we apply the existence theorems of solution for the stampacchia vector quasiequilibrium problems to study simultaneous solutions of caristi s fixed point theorem and the stampacchia set valued vector ekeland s variational principle our results on stampacchia set valued vector ekeland s variational principle are different from any existence results of these types of problems

extreme semilinear copulas abstract we study the extreme points in the krein milman sense of the class of semilinear copulas and provide their characterization related results into the more general setting of conjunctive aggregation functions i e semi copulas and quasi copulas are also presented

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

rearrangement inequalities for functionals with monotone integrands the inequalities of hardy littlewood and riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement it is known that these inequalities extend to integrands of the form f u1 um where f is supermodular in particular they hold when f has nonnegative mixed second derivatives i jf for all i j this paper concerns the regularity assumptions on f and the equality cases it is shown here that extended hardy littlewood and riesz inequalities are valid for supermodular integrands that are just borel measurable under some nondegeneracy conditions all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant i e measure preserving maps for the hardy littlewood inequality translations for the riesz inequality the proofs rely on monotone changes of variables in the spirit of sklar s theorem

ortholinear and paralinear semi copulas abstract a new method to construct semi copulas is introduced these semi copulas are called ortholinear resp paralinear semi copulas and their construction is based on linear interpolation on segments that are perpendicular resp parallel to the diagonal of the unit square the classes of ortholinear and paralinear quasi copulas are characterized as well

schur concave survival functions and survival analysis abstract barlow r e and f spizzichino schur concave survival functions and survival analysis journal of computational and applied mathematics 46 1993 437 447 we consider an n tuple of exchangeable nonnegative random variables which can e g be interpreted as lifetimes of n similar units and we assume that the joint survival function fn x1 xn p x1 x1 xn xn is in particular schur concave this condition is relevant since as it has been recently shown it provides a probabilistic model for aging in the subjectivist set up in this paper we analyze general properties of schur concave survival functions and give representation theorems in particular we study properties of schur concave survival distributions which are a finite population version of time transformed exponential distributions these distribution models are of interest in analyzing life data

meta theorems on inequalities for scalar fuzzy set cardinalities we present meta theorems stating general conditions ensuring that certain inequalities for cardinalities of ordinary sets are preserved under fuzzification when adopting a scalar approach to fuzzy set cardinality the conditions pertain to the commutative conjunctor used for modelling fuzzy set intersection in particular this conjunctor should fulfil a number of bell type inequalities the advantage of these meta theorems is that repetitious calculations can be avoided this is illustrated in the demonstration of the lukasiewicz transitivity of fuzzified versions of the simple matching coefficient and the jaccard coefficient or equivalently the triangle inequality of the corresponding dissimilarity measures

new constructions of diagonal patchwork copulas we present a method for constructing symmetric copulas which generalizes the diagonal patchwork construction of copulas procedure we also show how it is related to a new construction of a generalized farlie gumbel morgenstern distribution and to the copula transforms

sklar s theorem in an imprecise setting sklar s theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula when there is imprecision about the marginals we can model the available information by means of p boxes that are pairs of ordered distribution functions similarly we can consider a set of copulas instead of a single one we study the extension of sklar s theorem under these conditions and link the obtained results to stochastic ordering with imprecision

fixed points of commuting holomorphic mappings other than the wolff point let be the unit disc of c and let f g hol be such that f o g g o f for a 1 let fix a f p l lim r 1 f rp p lim r 1 f rp a we study the behavior of g on fix a f in particular we prove that g fix a f fix a f as a consequence besides conditions for fix a f fix a g 0 we prove a conjecture of c cowen in case f and g are univalent mappings

ekeland s variational principle for vectorial multivalued mappings in a uniform space abstract in this paper we establish ekeland s variational principle and an equilibrium version of ekeland s variational principle for vectorial multivalued mappings in the setting of separated sequentially complete uniform spaces our approaches and results are different from those in chen et al 2008 hamel 2005 and lin and chuang 2010 13 14 15 as applications of our results we study vectorial caristi s fixed point theorems and takahashi s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated sequentially complete uniform space we also apply our results to study maximal element theorems which are unified methods of several variational inclusion problems our results contain many known results in the literature fang 1996 21 and will have many applications in nonlinear analysis

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

ekeland type variational principle with applications to quasi variational inclusion problems abstract in this paper we study the ekeland type variational principle a caristi kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces by using these results we establish some existence results for solutions of quasi variational inclusion problems quasi optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces

iteration and the solution of functional equations for functions analytic in the unit disk this paper considers the classical functional equations of schroeder f o p xf and abel f o p f 1 and related problems of fractional iteration where 9p is an analytic mapping of the open unit disk into itself the main theorem states that under very general conditions there is a linear fractional transformation 4 and a function a analytic in the disk such that a oa p and that with suitable normalization 4 and a are unique in particular the hypotheses are satisfied if 4p is a probability generating function that does not have a double zero at 0 this intertwining relates solutions of functional equations for t to solutions of the corresponding equations for d for example it follows that if 4p has no fixed points in the open disk then the solution space of f o p xf is infinite dimensional for every nonzero x although the discrete semigroup of iterates of t usually cannot be embedded in a continuous semigroup of analytic functions mapping the disk into itself we find that for each z in the disk all sufficiently large fractional iterates of p can be defined at z this enables us to find a function meromorphic in the disk that deserves to be called the infinitesimal generator of the semigroup of iterates of p if the iterates of p can be embedded in a continuous semigroup we show that the semigroup must come from the corresponding semigroup for 4 and thus be real analytic in t the proof of the main theorem is not based on the well known limit technique introduced by koenigs 1884 but rather on the construction of a riemann surface on which an extension of 9p is a bijection much work is devoted to relating characteristics of p to the particular linear fractional transformation constructed in the theorem

supermigrative semi copulas and triangular norms a semi copula s 0 1 2 0 1 is called supermigrative if it is commutative and satisfies s ax y s x ay for all email protected 0 1 and for all x email protected 0 1 such that y

subnormality and composition operators on h2 if is a non constant analytic function defined on the unit disk d such that d d the composition operator c is the operator on the hardy space h2 of the unit disk defined by c f f in this paper we investigate the relationship between properties of the symbol and the subnormality of the operators c and c the main theorem shows under a regularity hypothesis that c is subnormal if and only if is in a restricted class of linear fractional transformations the two previously known special cases the affine transformations associated with the cesaro operator and the automorphisms are included as the extreme examples the proof of the main theorem consists of verifying a moment condition and yields in addition the construction of a measure that exhibits cgj as multiplication by an analytic function on p2 and the identification of the minimal normal extension as a weighted sum of shifts

equivalents to ekeland s variational principle in uniform spaces abstract a minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of pacific j math 55 2 1974 335 341 proc amer math soc 108 3 1990 707 714 two more equivalent formulations of the minimal element theorem are given it is applied to derive new versions of ekeland type theorems which improve results of j math anal appl 202 1996 398 412 finally the minimal element theorem is used to obtain an ekeland type theorem for functions with values in a linear space without topological structure

classification of semigroups of linear fractional maps in the unit ball we give a complete classiflcation up to conjugation of continuous semigroups of linear fractional self maps of the unit ball

generalized vector quasi equilibrium problems with applications in this paper we consider the generalized vector quasi equilibrium problem with or without involving condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems as applications of our results we derive some existence results for a solution to the vector quasi optimization problem for nondifferentiable functions and vector quasi saddle point problem

on fractional iterates of a brouwer homeomorphism embeddable in a flow we present a method for finding continuous and consequently homeomorphic orientation preserving iterative roots of a brouwer homeomorphism which is embeddable in a flow to obtain the roots we use a countable family of maximal parallelizable regions of the flow which is a cover of the plane the maximal parallelizable regions are unions of equivalence classes of an appropriate equivalence relation we show that if an equivalence class is invariant under the nth iterate of a brouwer homeomorphism g then it is invariant under g we use this fact to prove that each maximal parallelizable region of the flow must be invariant under all homeomorphic orientation preserving iterative roots of the given brouwer homeomorphism

existence theorems for variational inclusion problems and the set valued vector ekeland variational principle in a complete metric space abstract in this paper we apply an existence theorem for the variational inclusion problem to study the existence results for the variational intersection problems in ekeland s sense and the existence results for some variants of set valued vector ekeland variational principles in a complete metric space our results contain ekeland s variational principle as a special case and our approaches are different to those for any existence theorems for such problems

on a class of transformations of copulas and quasi copulas the theory of copulas is by now a very well established one recently larger classes of functions c 0 1 n 0 1 that are increasing in each variable and satisfy some conditions at the boundary like quasi copulas have been the object of fruitful research several authors have considered the action of a class of transformations on some aggregation operators as t norms copulas quasi copulas and so on these simple transformations do not preserve in general all properties of copulas or quasi copulas in particular the fact that only some properties are preserved by these transformations suggested the introduction of semi copulas the purpose of the present contribution is to give a fairly complete picture concerning such action on copulas and quasi copulas in particular we prove results concerning inclusions and strict inclusions among these classes of operators and those of their transforms

angular and unrestricted limits of one parameter semigroups in the unit disk abstract we study local boundary behaviour of one parameter semigroups of holomorphic functions in the unit disk earlier under some additional condition the position of the denjoy wolff point it was shown in 13 that elements of one parameter semigroups have angular limits everywhere on the unit circle and unrestricted limits at all boundary fixed points we prove stronger versions of these statements with no assumption on the position of the denjoy wolff point in contrast to many other problems in the question of existence for unrestricted limits it appears to be more complicated to deal with the boundary denjoy wolff point the case not covered in 13 than with all the other boundary fixed points of the semigroup

on maximal element theorems variants of ekeland s variational principle and their applications abstract in this paper we establish several different versions of generalized ekeland s variational principle and maximal element theorem for functions in complete metric spaces the equivalence relations between maximal element theorems generalized ekeland s variational principle generalized caristi s common fixed point theorems and nonconvex maximal element theorems for maps are also proved moreover we obtain some applications to a nonconvex minimax theorem nonconvex vectorial equilibrium theorems and convergence theorems in complete metric spaces

weighted composition semigroups on hardy spaces abstract the operator semigroups of the title are studied on hardy spaces conditions are found for strong continuity and the infinitesimal generator and its point spectrum are identified a particular semigroup is used to study an averaging operator

the stable subset of a univalent self map we give a complete description of the stable subset the union of all backward orbit with bounded step and of the pre models of a univalent self map f x rightarrow x where x is a kobayashi hyperbolic cocompact complex manifold such as the ball or the polydisc in mathbb c q the result is obtained studying the complex structure of a decreasing intersection of complex manifolds all biholomorphic to x

identity principles for commuting holomorphic self maps of the unit disc abstract let f g be two commuting holomorphic self maps of the unit disc if f and g agree at the common wolff point up to a certain order of derivatives no more than 3 if the wolff point is on the unit circle then f g

kendall distributions and level sets in bivariate exchangeable survival models for a given bivariate survival function f we study the relations between the set of the level curves of f and the kendall distribution then we characterize the survival models simultaneously admitting a specified kendall distribution and a specified set of level curves attention will be restricted to exchangeable survival models

semi copulas capacities and families of level sets we point out how capacities non additive measures can be used to provide explanations about the concept of bivariate ageing function the latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi copula

on a class of composition semigroups in hardy spaces the purpose of this note is to show that r 1 r is not always compact and then to give conditions for com pactness the separation of the semigroups giving rise to compact resolvent from those which do not seems to be very delicate our conditions are in terms of a certain associated univalent function to be introduced below

on the α migrativity of multivariate semi copulas in this paper we introduce and study the a migrative property for the class of multivariate semi copulas in particular a characterization of a migrative copulas is provided

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

mean growth of koenigs eigenfunctions in 1884 g koenigs solved schroeder s functional equation f o a af in the following context is a given holomorphic function mapping the open unit disk u into itself and fixing a point a e u f is holomorphic on u and a is a complex scalar koenigs showed that if 0 equation for p has a unique holomorphic solution cr satisfying a co p a a and o 0 1 moreover he showed that the only other solutions are the obvious ones given by constant multiples of powers of a we call a the koenigs eigenfunction of motivated by fundamental issues in operator theory and function theory we seek to understand the growth of integral means of koenigs eigenfunctions for 0 of to belong to the hardy space hp and show that the condition is necessary when is analytic on the closed disk for many mappings the condition may be expressed as a relationship between p a and derivatives of at points on ou that are fixed by some iterate of our work depends upon a formula we establish for the essential spectral radius of any composition operator on the hardy space hp department of mathematics washington and lee university lexington virginia 24450 e mail address pbourdonfwlu edu department of mathematics michigan state university east lansing michigan 48824 e mail address shapirofmath msu edu this content downloaded from 157 55 39 211 on sat 25 jun 2016 06 33 26 utc all use subject to http about jstor org terms

the koebe semigroup and a class of averaging operators on hp d we study on the hardy space h p the operators t f given by formule where f z is analytic on the unit disc d and has re f z 0 each such operator is closely related to a strongly continuous semigroup of weighted composition operators by studying first an extremal such semigroup the koebe semigroup we are able to obtain the upper bound t f p 2p re 1 f 0 im 1 f 0 for the norm we also show that t f is compact on h p if and only if the measure in the herglotz representation of 1 f is continuous

de finetti type representations for life distributions abstract beginning with a finite population of units and the judgment of exchangeability for units with respect to lifetime we argue that measures of similarity lead to the appropriate probabilistic models for aging this in turn implies that schur concavity of the joint probability function or more generally the joint survival distribution provides the correct probabilistic description of aging following this argument and using the principle of indifference we argue that the appropriate probability models for life distributions conditional on average life are in a family of distributions that we call the generalized gamma distributions if on the other hand we are interested in probabilistic models for aging conditional on average lifetime maintenance cost it follows from our development that generalized weibull distributions are appropriate

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

vectorial form of ekeland type variational principle with applications to vector equilibrium problems and fixed point theory abstract this paper introduces a vectorial form of equilibrium version of ekeland type variational principle some equivalent results to our variational principle are given as applications we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi metric spaces with a w distance caristi kirk fixed point theorem for multivalued maps is also established in a more general setting

ekeland s principle for vector equilibrium problems abstract in this paper the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones the aim is to provide a vector version of ekeland s theorem related to equilibrium problems to prove this principle a weak notion of continuity of a vector valued function is considered and some of its properties are presented via the vector ekeland s principle existence results for vector equilibria are proved in both compact and noncompact domains

extension of dependence properties to semi copulas and applications to the mean variance model this paper deals with the construction of a semi copula d not necessarily exchangeable whose dependence properties translate remarkable aspects of investors behavior to achieve this aim we propose a new version of the standard mean variance framework for our purpose a particular class of utility functions g has been introduced the induced transformation of g is considered and the definition of semi copula d hinges on the family of the indifference curves of g

commuting analytic functions let f and g not conformal automorphisms of the unit disk be analytic mappings of the unit disk into itself we say f and g commute if f o g g o f this paper characterizes those functions g that commute with a given function f several corollaries of this characterization give qualitative information about g given similar information about f and examples are given in each case to show the limitations of the conclusions some of the qualitative properties considered are univalence fixed point sets and whether two such g must commute with each other

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

second angular derivatives and parabolic iteration in the unit disk in this paper we deal with second angular derivatives at denjoy wolff points for parabolic functions in the unit disc namely we study and analyze the existence and the dynamical meaning of this second angular derivative for instance we provide several characterizations of that existence in terms of the so called koenigs function it is worth pointing out that there are two quite different classes of parabolic iteration those with positive hyperbolic step and those with zero hyperbolic step in the first case the koenigs function is in the caratheodory class but in the second case it is even unknown if it is normal therefore the ideas and techniques to approach these two cases are really different in the end we also present several rigidity results related to the second angular derivatives at denjoy wolff points

a concept of duality for multivariate exchangeable survival models in some past works by the author and collaborators the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed generally the ageing function turns out to be a semi copula here we focus attention on the special class of survival models whose ageing function is actually a copula for pairs of models in this class we define a notion of duality such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula the formulation of the notion of duality presented here came out some years ago in the frame of research activity in collaboration with bruno bassan

compactness of resolvent operators generated by a class of composition semigroups on hp consider a semigroup of composition operators t tf f circ phi t t geq 0 acting on the standard hardy space h p 1 leq p infty of the unit disk d assuming that the phi t have a common fixed point at 0 a unique univalent function h can be found such that h phi t z e ct h z z in d t geq 0 where c is a constant which is related to the infinitesimal generator a of t t in this paper the compactness of the resolvent operator r lambda a is studied using the function h it is shown that r lambda a is compact if and only if h lies in h q for each q infty in the cases where r lambda a is not compact it is shown that the spectrum of r lambda a contains a nontrivial disk a condition under which compactness of r lambda a implies compactness of the operators in t t is also obtained the methods used are function theoretic in particular the notion of a spiral like function plays a key role less

the studies of systems of variational inclusions problems and variational disclusions problems with applications abstract in this paper we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems from these existence results we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems

the role of generalized convexity in conic copula constructions abstract inspired by the notion of a conic semi copula we introduce upper conic lower conic and biconic semi copulas with a given section such semi copulas are constructed by linear interpolation on segments connecting the graph of a strict negation operator to the points 0 0 and or 1 1 the important subclasses of upper conic lower conic and biconic quasi copulas with a given section are characterized the notion of generalized convexity turns out to play a key role in this characterization some examples are also provided