on the completion of fuzzy metric spaces this paper discusses the completion of a fuzzy metric space in the sense of kaleva and seikkala that is modeled by a pair of two place functions l and r previous work on this question is based on l min r max under the condition that l and r are a generic class of two place functions we characterize the completable fuzzy metric space and show that the corresponding completion is uniquely determined up to isometry furthermore we point out that with more conditions on r including on r max the completion of each fuzzy metric space exists and is unique up to isometry this improves the corresponding result of kaleva the completion of fuzzy metric spaces j math anal appl 109 1985 194 198

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

a common fixed point theorem in a fuzzy metric space abstract we prove a common fixed point theorem for a sequence of mappings in a fuzzy metric space this result offers a generalization of grebiec s theorem m grebiec fuzzy sets and systems 27 1988 385 389

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

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

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

completeness in probabilistic quasi uniform spaces abstract in this paper we give a kind of cauchy completeness in probabilistic quasi uniform space by using pair filters and prove that this kind of cauchy completeness is equivalent to the completeness of induced probabilistic uniform space introduced by hohle we also give a characterization of cauchy completeness by lawvere completeness then we study the completion of probabilistic quasi uniform space and show that each t 0 separated probabilistic quasi uniform space has a t 0 cauchy completion finally in probabilistic quasi metric space we study the relationship between the completeness of induced quasi uniform space and the completeness of probabilistic quasi metric space

fuzzy pseudometric spaces vs fuzzifying structures in this paper we apply the representation theorem established in mardones perez and de prada vicente 2012 12 to define and study the degree in which some topological type properties of fuzzy pseudometric spaces are fulfilled fuzzifying structures which appear naturally are also investigated and the relation between these structures and fuzzy pseudometric spaces is explored

on some difference equations with eventually periodic solutions abstract we study the boundedness and the periodic character of the solutions of the equation formula where x 1 x 0 z and 1 1

fuzzy quasi metrics for the sorgenfrey line we endow the set of real numbers with a family of fuzzy quasi metrics in the sense of george and veeramani which are compatible with the sorgenfrey topology although these fuzzy quasi metrics are not deduced explicitly from a quasi metric they possess interesting properties related to completeness for instance we prove that they are balanced and complete in the sense of doitchinov and that only one of them is right k sequentially complete we also observe that compatible fuzzy quasi metrics for the sorgenfrey line cannot be left weakly right k sequentially complete

std convergence in fuzzy metric spaces in this note we answer two recent questions posed by morillas and sapena 10 related to standard convergence in fuzzy metric spaces in the sense of george and veeramani the obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of cauchyness

meir keeler theorems in fuzzy metric spaces abstract in this paper we propose the concept of fuzzy meir keeler contractive mappings in fuzzy metric spaces which covers fuzzy contractive mappings and fuzzy h contractive mappings as special cases with the aid of the proposed concept we obtain some meir keeler type fixed point theorems the derived theorems improve and extend the corresponding ones developed by d mihet d wardowski and v gregori et al and an example in the end of the paper illustrates the validity of our results

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

resonant frequency primitive waveforms and star waves in lattices for square and triangular lattices we have found a new line localized primitive waveform lpw existing at a resonant frequency in two dimensional 2d case the lpw represents a line of oscillating particles while the lattice outside this line remains at rest we show that a a single lpw does not conduct energy however a band consisting of two or more neighboring lpws is a conductor with the phase shift dependent energy flux velocity b any canonical sinusoidal wave consists of lpws in turn the lpw can be represented by a superposition of the sinusoidal waves these two types of waves are connected by the discrete fourier transform c there are two three lpw orientations for the square triangular lattice and this is why the sinusoidal wave group velocity orientation is piecewise constant at this frequency it coincides with the nearest lpw orientation d lpw can also exist at a lower frequency being localized at the lattice halfplane boundary further for 3d lattices plane localized waveforms are found to exist in a frequency region finally for the point harmonic excitation of 2d lattices we show that starlike waves develop with the rays in the lpw directions

an application of a representation theorem for fuzzy metrics to domain theory in this paper we study the interplay between fuzzy metric spaces and domain theory using the representation theorem established in mardones perez and de prada vicente 2012 12 we will prove that suitable restrictions of completeness in fuzzy metric spaces correspond to a structure of domain in the poset of formal balls endowed with appropriate orders

a note on compactness in a fuzzy metric space we study the compactness in a fuzzy metric space we also give a generalization of niemytzki tychonoff theorem for a fuzzy metric space

short communication some remarks on fuzzy contractive mappings recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of george and veeramani wardowski 2013 5 has been introduced here we provide some comments to this paper

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

the hausdorff fuzzy quasi metric removing the condition of symmetry in the notion of a fuzzy pseudo metric in kramosil and michalek s sense one has the notion of a fuzzy quasi pseudo metric then for each fuzzy quasi pseudo metric on a set x we construct a fuzzy quasi pseudo metric on the collection of all nonempty subsets of x called the hausdorff fuzzy quasi pseudo metric we investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words the notion of hausdorff fuzzy quasi pseudo metric when quasi pseudo metric fuzziness is considered in the sense of george and veeramani is also discussed

the effect on bending waves by defects in pinned elastic plates abstract this paper presents solutions to a number of problems posed for the out of plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations but that possess a finite number of defects we begin by considering a single one dimensional periodic array of pins we derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects central to approaching such problems is an understanding of bloch floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces the solutions to three problems are then sought the trapping of localised waves by a finite number of missing pins trapping of waves by entire rows of missing pins and the wave radiation pattern due to the forcing of a single pin all problems are treated analytically using bounded green s functions for thin elastic plates a discrete fourier transform solution method and simple explicit and rapidly convergent evaluations of the one and two dimensional lattice sums that arise

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

on contractions in probabilistic and fuzzy metric spaces in this paper by means of weakening conditions of the gauge function a new fixed point theorem for probabilistic contraction in menger probabilistic metric spaces with a t norm of h type is established this theorem improves and generalizes the recent results of iric 2010 4 jachymski 2010 12 and xiao et al 2013 25 by using the theorem we also obtain some important corollaries and the fixed point theorems for contraction in fuzzy metric spaces

iterated function systems and attractors in the km fuzzy metric spaces fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the km fuzzy metric spaces using the properties of hausdorff fuzzy metrics several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions in particular unbounded invariant sets are also examined for the iterated function systems in km fuzzy metric spaces our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces

l valued bornologies on powersets in m abel and a ostak 2011 1 the concept of an l fuzzy bornology was introduced actually an l fuzzy bornology on a set x is a certain ideal in the family lx of l fuzzy subsets of a set x here we propose an alternative approach to fuzzification of the concept of bornology we define an l valued bornology on a set x as an l fuzzy subset b of the powerset 2x satisfying l valued analogues of the axioms of a bornology basic properties of l valued bornological spaces are studied our special interest concerns l valued bornologies induced by fuzzy metrics and relative compactness type l valued bornologies in changgoguen l topological spaces

two classes of piecewise linear difference equations with eventual periodicity three in this paper we will study two classes of difference equations which are piecewise linear and of similar forms we will show that all nontrivial solutions of one equation are eventually periodic with prime period three we will show this result for one case of the second equation

on generalized fuzzy normed spaces and coincidence point theorems in this paper generalized fuzzy norms are defined on a set of objects endowed with a structure of linear space the relationships between these fuzzy norms and the fuzzy metrics and between these fuzzy norms and the topological structures on the base linear space are analyzed finally coincidence and fixed point theorems for mappings with values in fuzzy metric spaces and in such fuzzy normed spaces are proved

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

flexural waves in structured elastic plates mindlin versus bi harmonic models the paper presents an analytical approach to modelling of bloch floquet waves in structured mindlin plates the emphasis is given to a comparative analysis of two simplified plate models the classical kirchhoff theory and the mindlin theory for dynamic response of periodic structures it is shown that in the case of a doubly periodic array of cavities with clamped boundaries the structure develops a low frequency band gap in its dispersion diagram in the framework of the kirchhoff model this band gap persists even when the radius of the cavities tends to zero a clear difference is found between the predictions of kirchhoff and mindlin theories in mindlin theory the lowest band goes down to u 0 as the radius of the cavities tends to zero which is linked with the contrasting behaviour of the corresponding green functions

fixed point theorems and cauchy sequences in fuzzy metric spaces grabiec proved an analogue of banach contraction theorem in fuzzy metric spaces by using a fuzzy version of cauchy sequence some authors continued their work in the same direction of grabiec our aim in this paper is to discuss the difference between two different type of cauchy sequences used in the literature to prove fixed point theorems in fuzzy metric spaces

fuzzy quasi pseudometrics on algebraic structures abstract in this work we state a number of theorems about fuzzy quasi pseudometrizable algebraic structures our most useful results are 1 a fuzzy semitopological group whose topology is induced by a left invariant fuzzy quasi pseudometric then it is a fuzzy paratopological topological group 2 if the topology on a semigroup s is induced by an invariant fuzzy quasi pseudometric then s is a fuzzy topological semigroup and 3 the same conclusion is valid for a left invariant fuzzy quasi pseudometric on a monoid g such that the left translations are open and the right translations are continuous at the identity e of g by means of the standard fuzzy quasi pseudometric m d associated to a quasi pseudometric d our results apply in the case of semitopological groups semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes

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

fuzzy lipschitz maps and fixed point theorems in fuzzy metric spaces in this paper we introduce the notion of dilation and fuzzy lipschitz of a map from a fuzzy metric space into a fuzzy metric space and we prove continuity properties for such maps we also define the notion of the fuzzy lipschitz distance between two fuzzy metric spaces and show that two compact fuzzy metric spaces whose lipschitz distance is zero is fuzzy isometric to each other on the other hand we introduce the concept of minimal slope of a map between fuzzy metric spaces which is defined by the ratio of two fuzzy metrics and derive some properties on it and relations with the dilation in particular we show that if the dilation of a map from a fuzzy metric space which is complete in george and veeramani sense into itself is less than the minimal slope then the map must have a fixed point in case that a fuzzy metric space is considered in the sense of kramosil and michalek and that the completeness in the sense of grabiec the same result holds

fixed points in weak non archimedean fuzzy metric spaces mihet fuzzy j contractive mappings in non archimedean fuzzy metric spaces fuzzy sets and systems 159 2008 739 744 proved a theorem which assures the existence of a fixed point for fuzzy j contractive mappings in the framework of complete non archimedean fuzzy metric spaces motivated by this we introduce a notion of weak non archimedean fuzzy metric space and prove that the weak non archimedean fuzzy metric induces a hausdorff topology we utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings

the bicompletion of fuzzy quasi metric spaces extending the well known result that every fuzzy metric space in the sense of kramosil and michalek has a completion which is unique up to isometry we show that every km fuzzy quasi metric space has a bicompletion which is unique up to isometry and deduce that for each km fuzzy quasi metric space the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion

on fuzzy contractive mappings in fuzzy metric spaces some results on fuzzy contractive mappings in v gregori a sapena on fixed point theorems in fuzzy metric spaces fuzzy sets and systems 125 2002 245 253 are extended to edelstein fuzzy contractive mappings some new results are obtained by modifying the notion of convergence in fuzzy metric spaces due to specific axiom gv 2 in fuzzy metric spaces in the sense of george and veeramani this convergence is frechet

on the existence and the uniqueness of fixed points of sehgal contractions we discuss the problem of existence and uniqueness of fixed points for fuzzy contraction maps in fuzzy menger spaces and quasi pseudo menger spaces

on n polygonal interval value fuzzy sets and numbers abstract the structure of interval valued fuzzy sets is complex in regard to their arithmetic operations to reduce the computational complexity of arithmetic operations on interval valued fuzzy sets we propose the notion of an n polygonal interval valued fuzzy set considering two 2 n 2 tuple ordered real numbers complete representation of n polygonal interval valued fuzzy sets and numbers is provided moreover we demonstrate that the n polygonal interval valued fuzzy numbers can approximate the general interval value fuzzy numbers with any precision next we introduce arithmetic operations on n polygonal interval valued fuzzy numbers by capitalizing on the good characteristics of n polygonal interval valued fuzzy numbers the properties of the introduced arithmetic operations are also addressed in addition with the aid of a concrete example we verify the effectiveness of the approximation ability of the n polygonal interval valued fuzzy set furthermore we study the properties of the topological space of n polygonal interval valued fuzzy numbers this proves that this space is a complete separable and local compact metric space when endowed with the newly defined distance between two n polygonal interval valued fuzzy numbers by product it shows that arithmetic operations introduced here on n polygonal interval valued fuzzy numbers are continuous finally the practicability of n polygonal interval valued fuzzy numbers is verified by an example

comments on a common fixed point theorem in a fuzzy metric space our aim in this note is to point out that conditions of some fixed point theorems in a fuzzy metric space recently due to vasuki are inadequate and the proof of theorems are false

resolvent method for computations of localized defect modes of h polarization in two dimensional photonic crystals we have developed and tested a version of the resolvent or green s function method based on the shift inverse of the maxwellian operator that ensures stable convergence of iterative computations of localized defect modes of h polarization in two dimensional 2d photonic crystals the defect states are obtained by solving the eigenvalue problem for an associated compact operator with the expansion in bloch eigenfunctions of the unperturbed maxwellian operator this method can be extended to 3d photonic crystals we apply the method to a 2d square lattice of square dielectric rods in a dielectric background and compute with controlled precision of 1 the defect modes induced by the replacement of one rod the defect we investigate the rise and variation of the defect frequencies in a photonic band gap caused by the increase of the dielectric strength of the defect for four branches of localized modes of various symmetries

a difference equation with eventually periodic solutions we show that every solution of the difference equation xn 1 max 1xn axn 1 n 0 1 where the parameter a and the initial conditions x 1 and x0 are nonzero real numbers is eventually periodic with period 2 3 or 4 we also give a precise description of the period in terms of a and the initial conditions

on fixed point theorems in fuzzy metric spaces we give fixed point theorems for complete fuzzy metric spaces in the sense of george and veeramani and also for kramosil and michalek s fuzzy metric spaces which are complete in grabiec s sense

analytic theory of defects in periodically structured elastic plates we consider the problem of localized flexural waves in thin plates that have periodic structure consisting of a two dimensional array of pins or point masses changing the properties of the struct

towards probabilistic partial metric spaces diagonals between distance distributions abstract the quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories motivated by the categorical interpretation of partial metric spaces we are led to investigate the quantaloid of diagonals between distance distributions which is expected to establish the categorical foundation of probabilistic partial metric spaces observing that the quantale of distance distributions w r t an arbitrary continuous t norm is non divisible we precisely characterize diagonals between distance distributions and prove that one step functions are the only distance distributions on which the set of diagonals coincides with the generated down set

topological stability for fuzzy expansive maps abstract we introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces we show some basic properties of fuzzy expansive homeomorphisms moreover we prove walters s theorem in the context of fuzzy metric spaces i e a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable

on completable fuzzy metric spaces in this paper we construct a non completable fuzzy metric space in the sense of george and veeramani which allows to answer an open question related to continuity on the real parameter t in addition the constructed space is not strong non archimedean