on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

fixed points for fuzzy mappings in this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached a fuzzy mapping r over a set x is defined to be a function attaching to each x in x a fuzzy subset r of x an element x of x is called fixed point of r iff its membership degree to r is at least equal to the membership degree to r of any y x i e r r y y x two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described the convergence theorem of our algorithm is proved under the restrictive assumption that for any x in x the membership function of r has a complementary function examples of fuzzy mappings having this property are given but the problem of proving general criteria for a function to have a complementary remain open

the maximal distance between imprecise point objects in this paper we propose a new mathematical model of imprecise point objects and a new algorithm for determining the maximal distance between imprecise point objects results obtained with our model can be used in various applications such as gis imprecise spatial object modelling robotics environment models and image analysis imprecise feature extraction imprecise point objects are modelled as fuzzy points in linear fuzzy space linear fuzzy space is defined over r n where the membership function is convex upper semi continuous symmetric w r t the core and linearly decreasing w r t the core distance where the core is a single point a fuzzy convex hull is defined in linear fuzzy space the distance between objects points is modelled as an imprecise point object in linear fuzzy space defined over r 1 fuzzy ordering relations are defined in distance space the maximal distance is a fuzzy set over a set of distances the maximal distance between a set of imprecise point objects is then determined as the maximal distance of fuzzy convex hull edge points an algorithm for determining the maximal distance between imprecise points belonging to one and two dimensional linear fuzzy space is given for an exact calculation of this maximal distance computational complexity of the algorithm is of polynomial growth of the fourth degree however if the maximal distance is determined approximately then the algorithms computational complexity is of power growth of the quadratic degree with respect to the cardinality of the convex edge

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

quasiregular mappings in even dimensions o introduction 1 notation 2 some exterior algebra 3 differential forms in lnm i2 a n 4 differential systems for quasiregular mappings 5 liouville theorem in even dimensions 6 hodge theory in lp r n 7 the beltrami equation in even dimensions 8 the beurling ahlfors operator 9 regularity theorems for quasiregular mappings 10 the caccioppoli type estimate 11 removability theorems for quasiregular mappings 12 some examples appendix the 4 dimensional case

fuzzy mappings and fixed point theorems abstract we extend heilpern s fixed point theorem for fuzzy contraction mappings to a pair of generalized fuzzy contraction mappings also we prove a fixed point theorem for nonexpansive fuzzy mappings on a compact star shaped subset of a banach space

on the topological structure of km fuzzy metric spaces and normed spaces in this paper some relations among the axioms of km fuzzy metric spaces and km fuzzy normed spaces are discussed and some characterizations concerning the additional axiom are given also a quasi metric family and a quasi norm family corresponding respectively to the km fuzzy metric spaces and the km fuzzy normed spaces are introduced and studied using their properties the different topological structures of km fuzzy metric spaces and km fuzzy normed spaces with variable t norm are described and some new properties on these spaces are obtained as their special cases the topological structures and properties concerning gv fuzzy metric spaces and gv fuzzy normed spaces are presented

regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps let omega subset mathbb r n n ge 2 be open and n subset mathbb r k a smooth compact riemannian manifold without boundary we consider the approximated harmonic map equation delta u a u nabla u nabla u f for maps u in h 1 omega n where f in l p omega mathbb r k for p frac n 2 we prove holder continuity for weak solution s which satisfy a certain smallness condition for p frac n 2 we derive an energy estimate which allows to prove partial regularity for stationary solutions of the heat flow for harmonic maps in dimension n le 4

fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces abstract this paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces by virtue of this concept some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained these new results are a unified approach to generalize several fixed point theorems for fuzzy mappings

fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces abstract using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved as an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

fixed point theorems for fuzzy numbers abstract in this paper we study the problem of the existence of fixed points for fuzzy maps we first define uniform structures on sets of fuzzy subsets and describe the closed convergence and myope convergence structures which have properties close to the corresponding traditional ones we then give two ways in order to obtain fixed point results we finally give applications of these results particularly to fuzzy markov processes

minimization theorems for fixed point theorems in fuzzy metric spaces and applications abstract in this paper we establish a minimization theorem in fuzzy metric spaces and make use of the result to obtain a fixed point theorem in fuzzy metric spaces which is similar to the downing kirk fixed point theorem in metric spaces as the consequences we obtain caristi s fixed point theorem and ekeland s variational principle in fuzzy metric spaces and also give a direct simple proof of the equivalence between these two theorems some applications of these results to probabilistic metric spaces are presented

the qualitative behavior at the free boundary for approximate harmonic maps from surfaces let u n be a sequence of maps from a compact riemann surface m with smooth boundary to a general compact riemannian manifold n with free boundary on a smooth submanifold k subset n satisfying begin aligned sup n left vert nabla u n vert l 2 m vert tau u n vert l 2 m right le lambda end aligned where tau u n is the tension field of the map u n we show that the energy identity and the no neck property hold during a blow up process the assumptions are such that this result also applies to the harmonic map heat flow with free boundary to prove the energy identity at finite singular time as well as at infinity time also the no neck property holds at infinity time

partial regularity for stationary harmonic maps at a free boundary let and be smooth riemannian manifolds of the dimension n 2 with nonempty boundary and compact without boundary we consider stationary harmonic maps u h 1 with a free boundary condition of the type u given a submanifold we prove partial boundary regularity namely sing u 0 a result that was until now only known in the interior of the domain see b the key of the proof is a new lemma that allows an extension of u by a reflection construction once the partial regularity theorem is known it is possible to reduce the dimension of the singular set further under additional assumptions on the target manifold and the submanifold

fixed point theorems in fuzzy metric spaces using property e a abstract we prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using e a property

fixed point theorems for fuzzy mappings abstract this paper presents some new fixed point theorems for fuzzy mappings the results given in this paper improve and extend some recent results

fuzzy contractive mappings and fixed points in fuzzy metric spaces in the paper we introduce a new concept of fuzzy contraction which is a generalization of a fuzzy contractive mapping initiated in the article v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 252 for this type of contraction the conditions guaranteeing the existence of fixed point in fuzzy m complete metric spaces in the sense of george and veeramani are established the result is supported by examples

coincidence theorems for set valued mappings and ekeland s variational principle in fuzzy metric spaces abstract in this paper we establish a coincidence theorem for set valued mappings in fuzzy metric spaces with a view to generalizing downing kirk s fixed point theorem in metric spaces as consequences we obtain caristi s coincidence theorem for set valued mappings and a more general type of ekeland s variational principle in fuzzy metric spaces further we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces some applications of these results to probabilistic metric spaces are presented

fracture flow simulation using a finite difference lattice boltzmann method we present numerical computations for single phase flow through three dimensional digitized rock fractures under varied simulated confining pressures appropriate to midcrustal depths the computations are performed using a finite difference lattice boltzmann method and thus simulate navier stokes flow the digitized fracture data sets come from profiled elevations taken on tensile induced fractures in harcourt granite numerical predictions of fracture permeability are compared with laboratory measurements performed on the same fractures use of the finite difference lattice boltzmann method allows computation on nonuniform grid spacing enabling accurate resolution across the aperture width without extensive refinement in the other two directions

coincidence point theorems and minimization theorems in fuzzy metric spaces abstract in this paper some new versions of coincidence point theorems and minimization theorems for single valued and multi valued mappings in generating spaces of the quasi metric family are obtained as applications we utilize our main theorems to prove coincidence point theorems fixed point theorems and minimization theorems for single valued and multi valued mappings in fuzzy metric spaces and probabilistic metric spaces

partially constrained boundary conditions with energy minimizing mappings on considere la regularite a la frontiere pour une application minimisant l energie u m n pour deux types de conditions aux limites frontiere libre et condition limite partiellement contrainte

coincidence point theorems in probabilistic and fuzzy metric spaces in this paper we prove some new coincidence point theorems for a hybrid pair of single and multi valued mappings under more generalized contractive conditions in menger spaces and generalized menger spaces our results can be applied to the theory of the fuzzy metric spaces by relaxing some conditions several recent results given by zikic dos enovic mihet and ghaemi and razani are extended

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek

on fixed point theorems in fuzzy metric spaces abstract the purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces the results presented improve and generalize some recent results

boundary equations and regularity theory for geometric variational systems with neumann data we study boundary regularity of maps from two dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which at the boundary intersect perpendicularly with a support manifold for example harmonic maps or h surfaces with a partially free boundary condition in the interior it is known by the celebrated work of riviere that these maps satisfy a system with an antisymmetric potential from which one can derive the interior regularity of the solution avoiding a reflection argument we show that these maps satisfy along the boundary a system of equations which also exhibits a nonlocal antisymmetric potential that combines information from the interior potential and the geometric neumann boundary condition we then proceed to show boundary regularity for solutions to such systems