mizoguchi takahashi s fixed point theorem is a real generalization of nadler s abstract we give an example which says that mizoguchi takahashi s fixed point theorem for set valued mappings is a real generalization of nadler s we also give a very simple proof of mizoguchi takahashi s theorem

corrigendum to coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions j comput appl math 283 2015 201 217 abstract in a recent paper h k pathak r p agarwal y j cho coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions j comput appl math 283 2015 201 217 the authors have studied some problems on coincidence points and fixed points of multi valued mappings in order to illustrate the generality of their main result theorem 3 2 with respect to older related results nadler s berinde berinde mizoguchi takahashi and du s fixed point theorem the authors presented two examples i e examples 3 3 and 3 4 the main aim of this note is to show that example 3 3 fails in proving the generality of theorem 3 2 over berinde berinde s fixed point theorem

approximation of biholomorphic mappings by automorphisms of cn in this paper we prove several results on approximation of biholomorphic mappings between domains in c n 2 by holomorphic automorphisms of c recall that the group of holomorphic automorphisms of c denoted aut c consists of those holomorphic mappings c c that have a holomorphic inverse 4 1 c c with the topology of uniform convergence on compact sets aut c is a topological group while the group aut c 1 of automorphisms of the complex plane consists only of the linear mappings az b a b e c a 4 0 the group aut c is very large and complicated when n 2 let us choose a linear coordinate system on c and write the coordinates as z z w where z z1 zn i c c n 1 and w z c then autc n contains mappings of the form

embedding complete holomorphic discs through discrete sets abstract let be the open unit disc in c and let b be the open unit ball in c 2 we prove that every discrete subset of b is contained in the range of a complete proper holomorphic embedding b

fixed point theorems for set valued contractions in complete metric spaces abstract the fixed point theory of set valued contractions which was initiated by nadler s b nadler jr multi valued contraction mappings pacific j math 30 1969 475 488 was developed in different directions by many authors in particular by s reich fixed points of contractive functions boll unione mat ital 5 1972 26 42 n mizoguchi w takahashi fixed point theorems for multivalued mappings on complete metric spaces j math anal appl 141 1989 177 188 y feng s liu fixed point theorems for multi valued contractive mappings and multi valued caristi type mappings j math anal appl 317 2006 103 112 in the present paper the concept of contraction for set valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established one of our results essentially generalizes the nadler and feng liu theorems and is different from the mizoguchi takahashi result the second result is different from the reich and mizoguchi takahashi results the method used in the proofs of our results is inspired by mizoguchi takahashi and feng liu s ideas comparisons and examples are given

volumes of balls in large riemannian manifolds we prove two lower bounds for the volumes of balls in a riemannian manifold if m n g is a complete riemannian manifold with lling radius at least r then it contains a ball of radius r and volume at least n r n if m n hyp is a closed hyperbolic manifold and if g is another metric on m with volume no greater than n vol m hyp then the universal cover of m g contains a unit ball with volume greater than the volume of a unit ball in hyperbolic n space

some new results and generalizations in metric fixed point theory abstract the main purpose of this paper is the study of the generalization of some results given in m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl 326 2007 772 782 and references therein some generalizations of the mizoguchi takahashi fixed point theorem kannan s fixed point theorems and chatterjea s fixed point theorems are established by using our new fixed point theorems

holomorphic functions unbounded on curves of finite length given a pseudoconvex domain open image in new window we prove that there is a holomorphic function f on d such that the lengths of paths p 0 1 rightarrow d along which mathfrak r f is bounded above with p 0 fixed grow arbitrarily fast as p 1 rightarrow bd a consequence is the existence of a complete closed complex hypersurface m subset d such that the lengths of paths p 0 1 rightarrow m with p 0 fixed grow arbitrarily fast as p 1 rightarrow bd

fixed points of generalized contractive multi valued mappings in a recent paper n mizoguchi and w takahashi gave a positive answer to the conjecture of s reich concerning the existence of fixed points of multi valued mappings that satisfy a certain contractive condition in this paper we provide an alternative and somewhat more straightforward proof for the theorem of mizoguchi and takahashi also the problems associated with fixed points of weakly contractive multi valued mappings are studied finally we make a few comments that improve other results from their paper j math anal appl 141 1989 177 188

null curves in mathbb c 3 and calabi yau conjectures for any open orientable surface m and convex domain omega subset mathbb c 3 there exist a riemann surface n homeomorphic to m and a complete proper null curve f n this result follows from a general existence theorem with many applications among them the followings for any convex domain in mathbb c 2 there exist a riemann surface n homeomorphic to m and a complete proper holomorphic immersion f n furthermore if d subset mathbb r 2 is a convex domain and is the solid right cylinder x in mathbb c 2 mbox re x in d then f can be chosen so that re f n d is proper there exist a riemann surface n homeomorphic to m and a complete bounded holomorphic null immersion f n to rm sl 2 mathbb c there exists a complete bounded cmc 1 immersion x m to mathbb h 3 for any convex domain omega subset mathbb r 3 there exists a complete proper minimal immersion xj j 1 2 3 m with vanishing flux furthermore if d subset mathbb r 2 is a convex domain and omega x j j 1 2 3 in mathbb r 3 x 1 x 2 in d then x can be chosen so that x1 x2 m d is proper any of the above surfaces can be chosen with hyperbolic conformal structure

on a general class of multi valued weakly picard mappings abstract the concept of weak contraction from the case of single valued mappings is extended to multi valued mappings and then corresponding convergence theorems for the picard iteration associated to a multi valued weak contraction are obtained the main results in this paper extend improve and unify a multitude of classical results in the fixed point theory of single and multi valued contractive mappings and also improve recent results from the paper p z daffer h kaneko fixed points of generalized contractive multi valued mappings j math anal appl 192 1995 655 666

pinching constants for hyperbolic manifolds we show in this paper that for everyn 4 there exists a closedn dimensional manifoldv which carries a riemannian metric with negative sectional curvaturek but which admits no metric with constant curvaturek 1 we also estimate the pinching constantsh for which our manifoldsv admit metrics with 1 k h

a foliation of the ball by complete holomorphic discs we show that the open unit ball mathbb b n of mathbb c n n 1 admits a nonsingular holomorphic foliation by complete properly embedded holomorphic discs

a properly embedded holomorphic disc in the ball with finite area and dense boundary in this paper we construct a properly embedded holomorphic disc in the unit ball mathbb b 2 of mathbb c 2 having a surprising combination of properties on the one hand it has finite area and hence is the zero set of a bounded holomorphic function on mathbb b 2 on the other hand its boundary curve is everywhere dense in the sphere b mathbb b 2 a similar result is proved in higher dimensions our construction is based on an approximation result in contact geometry also proved in the paper

construction of labyrinths in pseudoconvex domains we build in a given pseudoconvex runge domain d of mathbb c n an mathcal o d convex set gamma every connected component of which is a holomorphically contractible convex compact set enjoying the property that any continuous path gamma 0 1 rightarrow d with lim r rightarrow 1 gamma r in partial d and omitting gamma has infinite length this solves a problem left open in a recent paper by alarcon and forstneric

fixed point theorems for multivalued mappings on complete metric spaces on obtient une version multivaluee du theoreme de point fixe de caristi qui est equivalent au principe e variationnel du a ekeland on utilise ce resultat pour obtenir un theoreme qui deduit le theoreme de nadler et un theoreme de point fixe commun pour une application a 1 valeur et une application multivaluee

growth of balls in the universal cover of surfaces and graphs in this paper we prove uniform lower bounds on the volume growth of balls in the universal covers of riemannian surfaces and graphs more precisely there exists a constant 0 such that if m hyp is a closed hyperbolic surface and h another metric on m with area m h area m hyp then for every radius r 1 the universal cover of m h contains an r ball with area at least the area of an r ball in the hyperbolic plane this positively answers a question of l guth for surfaces we also prove an analog theorem for graphs

every bordered riemann surface is a complete conformal minimal surface bounded by jordan curves in this paper we find approximate solutions of certain riemann hilbert boundary value problems for minimal surfaces in r and null holomorphic curves in c for any n 3 with this tool in hand we construct complete conformally immersed minimal surfaces in r which are normalized by any given bordered riemann surface and have jordan boundaries we also furnish complete conformal proper minimal immersions from any given bordered riemann surface to any smoothly bounded strictly convex domain of r which extend continuously up to the boundary for n 5 we find embeddings with these properties

complete proper holomorphic embeddings of strictly pseudoconvex domains into balls abstract we construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with c 2 boundary in c n into the unit ball of c n for n large enough thereby answering a question of alarcon and forstneric 2013

systoles des surfaces plates singulieres de genre deux the extremal metrics for the isosystolic problem on surfaces of genus two are studied in this paper we show that contrary to e calabi s conjecture in genus three no flat metric with conical singularities is extremal for this problem in genus two

a complete complex hypersurface in the ball of c n in 1977 p yang asked whether there exist complete immersed complex submanifolds m k c n with bounded image a positive answer is known for holomorphic curves k 1 and partial answers are known for the case when k 1 the principal result of the present paper is a construction of a holomorphic function on the open unit ball bn of c n whose real part is unbounded on every path in bn of nite length that ends on bbn a consequence is the existence of a complete closed complex hypersurface in bn this gives a positive answer to yang s question in all dimensions k n 1 k n by providing properly embedded complete complex manifolds

coincidence and fixed points for multi valued mappings and its application to nonconvex integral inclusions in this paper we consider some problems on coincidence point and fixed point theorems for multi valued mappings applying the characterizations of p functions we establish some new existence theorems for coincidence point and fixed point distinct from nadler s fixed point theorem berinde berinde s fixed point theorem mizoguchi takahashi s fixed point theorem and du s fixed point theorem for nonlinear multi valued contractive mappings in complete metric spaces our results compliment and extend the main results given by some authors in the literature in the sequel we consider a nonconvex integral inclusion and prove the filippov type existence theorem by using an appropriate norm on the space of selection of a multi function and a multi valued contraction for set valued mappings

the calabi yau problem null curves and bryant surfaces in this paper we prove that every bordered riemann surface m admits a complete proper null holomorphic embedding into a ball of the complex euclidean 3 space mathbb c 3 the real part of such an embedding is a complete conformal minimal immersion m rightarrow mathbb r 3 with bounded image for any such m we also construct proper null holomorphic embeddings m hookrightarrow mathbb c 3 with a bounded coordinate function these give rise to properly embedded null curves m hookrightarrow sl 2 mathbb c and to properly immersed bryant surfaces m rightarrow mathbb h 3 in the hyperbolic 3 space in particular we provide the first examples of proper bryant surfaces with finite topology and of hyperbolic conformal type the main novelty when compared to the existing results in the literature is that we work with a fixed conformal structure on m this is accomplished by introducing a conceptually new method based on complex analytic techniques one of our main tools is an approximate solution to certain riemann hilbert boundary value problems for null curves in mathbb c 3 developed in sect 3

every bordered riemann surface is a complete proper curve in a ball we prove that every bordered riemann surface admits a complete proper holomorphic immersion into a ball of mathbb c 2 and a complete proper holomorphic embedding into a ball of mathbb c 3