stability of cauchy jensen type functional equation in generalized fuzzy normed spaces in this paper we establish some stability results concerning the cauchy jensen functional equation in generalized fuzzy normed spaces the results of the present paper improve and extend some recent results

on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

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

the completion of a fuzzy normed linear space abstract the concept of a fuzzy normed linear space was introduced in an earlier paper by the author finite dimensional fuzzy normed linear space fuzzy sets and systems 48 1992 239 248 it was shown therein that any finite dimensional fuzzy normed linear space is necessarily complete there do exist incomplete fuzzy normed linear spaces incompleteness is shown to have handicaps see section 3 there is a need for completion in the sense of enlarging the incomplete space so that the given space is embedded in the enlarged space it is shown in this paper see theorem 3 that this is really possible

generic mean curvature flow i generic singularities it has long been conjectured that starting at a generic smooth closed embedded surface in r 3 the mean curvature ow remains smooth until it arrives at a singularity in a neighborhood of which the ow looks like concentric spheres or cylinders that is the only singularities of a generic ow are spherical or cylindrical we will address this conjecture here and in a sequel the higher dimensional case will be addressed elsewhere the key to showing this conjecture is to show that shrinking spheres cylinders and planes are the only stable self shrinkers under the mean curvature ow we prove this here in all dimensions an easy consequence of this is that every singularity other than spheres and cylinders can be perturbed away

error probability analysis of bit interleaved coded modulation this correspondence presents a simple method to accurately compute the error probability of bit interleaved coded modulation bicm thanks to the binary input output symmetric bios nature of the channel the pairwise error probability pep is equal to the tail probability of a sum of random variables with a particular distribution this probability is in turn computed with a saddlepoint approximation its precision is numerically validated for coded transmission over standard gaussian noise and fully interleaved fading channels for both convolutional and turbo like codes

a fixed point approach to almost quartic mappings in quasi fuzzy normed spaces we will define a notion for a quasi fuzzy p normed space then we use the fixed point alternative theorem to establish hyers ulam rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p normed space later we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function control function and the unique quartic mapping which approximates the almost quartic map finally some applications of our results in the stability of quartic mappings from a linear space into a quasi p norm space will be exhibited

on the uniform boundedness theorem in fuzzy quasi normed spaces we prove that a family of continuous linear operators from a fuzzy quasi normed space of the half second category to a fuzzy quasi normed space is uniformly fuzzy bounded if and only if it is pointwise fuzzy bounded this result generalizes and unifies several well known results in fact the classical uniform boundedness principle or banach steinhauss theorem is deduced as a particular case furthermore we establish the relationship between uniform fuzzy boundedness and equicontinuity which allows us to give a uniform boundedness theorem in the class of paratopological vector spaces the classical result for topological vector spaces is deduced as a corollary

bounds on the capacity region of the optical intensity multiple access channel this paper provides new inner and outer bounds on the capacity region of the optical intensity multiple access channel oimac with a per user average or peak power constraint for the average power constrained oimac our bounds at high power are asymptotically tight thereby characterizing the asymptotic capacity region the bounds are extended to the k user oimac with an average power constraint without loss of asymptotic optimality for the peak power constrained oimac at high power we bound the asymptotic capacity region to within 0 09 bits and determine the asymptotic capacity region in the symmetric case at moderate power for both types of constraints the capacity regions are bounded to within fairly small gaps

metrization theorems in l topological spaces abstract in this paper some characterizations of a pointwise uniformity are presented in l fuzzy set theory a new hausdorff separation axiom compatible with pointwise metric is introduced urysohn metrization theorem and alexandroff urysohn metrization theorem in general topology are generalized to l topology

fuzzy bounded linear operators in felbin s type fuzzy normed linear spaces in this paper definitions of strongly fuzzy bounded linear operator and weakly fuzzy bounded linear operators are given and the idea of their fuzzy norms are introduced the concept of fuzzy dual spaces are introduced and the hahn banach theorem is established in fuzzy setting

fuzzy real numbers abstract the paper gives a contribution to the study of fuzzy real numbers continuing that in eklund and gahler 1988 gahler and gahler 1992 and gahler 1992 we start with investigating algebraic properties using two types of decompositions of fuzzy numbers and the notions of fuzzy norm of symmetric difference and of supplements of fuzzy numbers by means of these notions two special fuzzy metrics on the fuzzy real line are given the fuzzy distance function d and the extended fuzzy distance function d the main interest concerns fuzzy topological properties of the fuzzy real line in particular there are studied the fuzzy topologies t t d and t d t is closely related to the fuzzy topology of hutton s fuzzy unit interval and t d and t d are canonically generated by the fuzzy metrics d and d respectively

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

fuzzy pseudo norms and fuzzy f spaces in the present paper we firstly introduce the notion of fuzzy pseudo norm then we extend improve and complete the results obtained by t bag and s k samanta for fuzzy norms in the fuzzy pseudo norms context lastly we introduce and discuss the notions of fuzzy f norm and fuzzy f space by means of several auxiliary results we obtain a characterization of metrizable topological linear spaces in terms of fuzzy f norm

some fixed point theorems in fuzzy normed linear spaces in this paper the concepts of sectional fuzzy continuous mappings l fuzzy compact sets asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced schauder type and other fixed point theorems have been established in fuzzy normed linear spaces

perturbation of generalized derivations in fuzzy menger normed algebras in this paper we introduce a notion for fuzzy menger normed algebra then we will investigate continuity of algebraic operations in this space we will show that the class of all fuzzy menger normed algebras strictly contains the class of normed algebras finally we will prove hyers ulam rassias superstability of generalized derivation functional equationf ax by vw af x bf y vf w g v w x y v email protected x 0 a email protected c in complete fuzzy menger normed algebras a few applications of our results will be exhibited

fuzzy stability of a functional equation associated with inner product spaces moslehian et al investigated the fuzzy stability problems for the cauchy additive functional equation and the jensen additive functional equation in fuzzy banach spaces in this paper we prove the generalized hyers ulam stability of a functional equation associated with inner product spaces in fuzzy banach spaces

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

short communication a note on the definition of a generalized fuzzy normed space we reconsider the definition of a generalized fuzzy normed space from i golet on generalized fuzzy normed spaces and coincidence point theorems fuzzy sets and systems 161 2010 1138 1144 showing that the mapping used in the homogeneity axiom must satisfy the multiplicative cauchy functional equation therefore generalized fuzzy normed spaces are in fact fuzzy p normed spaces with p 0

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

fuzzy approximately cubic mappings we establish some stability results concerning the cubic functional equationf 2x y f 2x y 2f x y 2f x y 12f x in fuzzy normed spaces we discuss the fuzzy continuity of the cubic mappings and show that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed space

a comparative study of fuzzy norms on a linear space in this paper a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that broadly they may be classified into two types one of which is katsaras s type and the other is felbin s type

on convex and concave fuzzy mappings abstract in this paper we introduce the concepts of convex subsets of f 0 the set of all fuzzy numbers and monotonic fuzzy mappings on r2 and show that a monotonic fuzzy mapping f on a convex set c r1 or r2 is quasi convex and quasi concave we establish two characterizations for convex fuzzy mappings and two characterizations for concave fuzzy mappings we also prove the least upper bound property

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

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

approximation properties in fuzzy normed spaces the paper is concerned with approximation properties which are defined in fuzzy normed spaces first we introduce the approximation property and the bounded approximation property next we provide two main examples first example is a fuzzy normed space that does not have the approximation property and second example is a fuzzy normed space with the approximation property that does not have the bounded approximation property finally we provide characterizations of approximation properties in fuzzy normed spaces

blow up and global existence for heat flows of harmonic maps in this paper it is proved that the solution to the evolution problem for harmonic maps blows up in finite time if the initial map belongs to some nontrivial homotopy class and the initial energy is sufficiently small

bit interleaved coded modulation revisited a mismatched decoding perspective we revisit the information theoretic analysis of bit interleaved coded modulation bicm by modeling the bicm decoder as a mismatched decoder the mismatched decoding model is well defined for finite yet arbitrary block lengths and naturally captures the channel memory among the bits belonging to the same symbol we give two independent proofs of the achievability of the bicm capacity calculated by caire et al where bicm was modeled as a set of independent parallel binary input channels whose output is the bitwise log likelihood ratio our first achievability proof uses typical sequences and shows that due to the random coding construction the interleaver is not required the second proof is based on the random coding error exponents with mismatched decoding where the largest achievable rate is the generalized mutual information moreover the generalized mutual information of the mismatched decoder coincides with the infinite interleaver bicm capacity we show that the error exponent and hence the cutoff rate of the bicm mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite interleaved model for binary reflected gray mapping in gaussian channels the loss in error exponent is small we also consider the mutual information appearing in the analysis of iterative decoding of bicm with extrinsic information transfer exit charts if the symbol metric has knowledge of the transmitted symbol exit mutual information admits a representation as a pseudo generalized mutual information which is in general not achievable a different symbol decoding metric for which the extrinsic side information refers to the hypothesized symbol induces a generalized mutual information lower than the coded modulation capacity in this case perfect extrinsic side information turns the mismatched decoder error exponent into that of coded modulation

beta beta bounds finite blocklength analog of the golden formula it is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution a relation sometimes referred to as the golden formula this paper is concerned with a finite blocklength extension of this relation this extension consists of two elements 1 a finite blocklength channel coding converse bound by polyanskiy and verdu which involves the ratio of two neyman pearson beta functions beta beta converse bound and 2 a novel beta beta channel coding achievability bound expressed again as the ratio of two neyman pearson beta functions to demonstrate the usefulness of this finite blocklength extension of the golden formula the beta beta achievability and converse bounds are used to obtain a finite blocklength extension of verdu s wideband slope approximation the proof parallels the derivation of the latter with the beta beta bounds used in place of the golden formula the beta beta achievability bound is also shown to be useful in cases where the capacity achieving output distribution is not a product distribution due to e g a cost constraint or structural constraints on the codebook such as orthogonality or constant composition as an example the bound is used to characterize the channel dispersion of the additive exponential noise channel and to obtain a finite blocklength achievability bound the tightest to date for multiple input multiple output rayleigh fading channels with perfect channel state information at the receiver

schauder bases and approximation property in fuzzy normed spaces our aim in this article is to introduce and study the notion of weak and strong schauder bases in fuzzy normed spaces further we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces

fuzzy versions of hyers ulam rassias theorem we introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces more precisely we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense

fuzzy inner product spaces in this paper we show that all results obtained recently on fuzzy inner product spaces are obvious to achieve this goal we modify the definition of the fuzzy inner product space and then we mention and prove some monotonicity and orthogonality properties of the new fuzzy inner product space finally we describe fuzzy inner products in terms of families of crisp inner products namely any fuzzy inner product corresponds to a family of crisp inner products and vice versa

nearest neighbor decoding for additive non gaussian noise channels we study the performance of a transmission scheme employing random gaussian codebooks and nearest neighbor decoding over a power limited additive non gaussian noise channel we show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white gaussian noise channel with signal and noise power equal to those of the original channel the results are presented for single user channels as well as multiple access channels and are extended to fading channels with side information at the receiver

the theory of global fuzzy neighborhood structures iii fuzzy uniform structures in this paper a new notion of fuzzy uniform structure is presented and investigated fuzzy uniform structures are given as special fuzzy filters of special interest are those fuzzy uniform structures which are sup fuzzy filters they can be characterized by a related notion of fuzzy syntopogenous structure as is shown fuzzy metrics gahler and gahler 1994 generate fuzzy uniform structures in our sense each fuzzy uniform structure has an associated global homogeneous fuzzy neighborhood structure and hence also an associated fuzzy topology in case of a 0 1 fuzzy uniform structure and even in a more general case a fuzzy uniform structure of the first type can be associated there are given relation to huttons s and katsaras notions of fuzzy uniform structure hutton 1977 katsaras 1979 and to the notion of fuzzy syntopogenous structure in sense of katsaras and petalas 1984

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

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

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

schauder bases in banach spaces application to numerical solutions of differential equations abstract in this work we present a numerical method for approximating the solution of a linear differential problem we formulate a general problem in a banach space making use of a schauder basis and the tau method to approximate the load function and the solution of the differential problem finally we offer a numerical example

separation of fuzzy normed linear spaces abstract this paper deals with hausdorff separation axiom for fuzzy topological spaces the necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated properties of separated and non separated fuzzy norms along with examples are studied separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised separation of quotient fuzzy semi norm is studied

characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy quasi norms we obtain characterizations of those paratopological vector spaces that are quasi metrizable locally bounded quasi metrizable locally convex and quasi normable respectively in terms of appropriate kinds of fuzzy quasi norms characterizations of distinguished kinds of metrizable topological vector spaces some of them known already are deduced as particular cases of our approach

convergence in the i fuzzy real line infinite sums and sequences in the fuzzy real line have been investigated by wang in this paper a necessary and sufficient condition for a sequence in to be convergent is given in terms of cut set it is proved that fuzzy convergence of sequences in is equivalent to weak convergence as an application convergence of sequences of fuzzy numbers in the sense of chang and zadeh is discussed

communication by energy modulation the additive exponential noise channel communication across an additive exponential noise aen channel is studied the aen channel is derived from a continuous time gaussian channel by assuming decoherence between the signal and noise components decoherence renders impossible the use of the complex amplitude and information is transmitted by modulating the signal energy the aen channel is shown to perform closely in terms of channel information rate and error probability of binary codes including the use of bit interleaved coded modulation to an equivalent discrete time gaussian channel of identical signal to noise ratio constellations are designed for low signal to noise ratios where the minimum energy per bit is not universally attained by all modulations and for high signal to noise ratios where an equiprobable nonuniform constellation 0 76 db away from capacity is described the multiple access aen channel is also considered its capacity region coincides with that of the gaussian equivalent feedback does not however enlarge the capacity region

statistical convergence in fuzzy normed linear spaces in this paper we introduce the notions of statistically convergent sequence and statistically cauchy sequence in a fuzzy normed linear space fns and establish some basic facts we also define statistical limit points and statistical cluster points of a sequence in an fns and investigate the relations between these concepts

a comment on the completion of fuzzy metric spaces we argue that in some recent papers discussing the completion of fuzzy metric and fuzzy normed spaces proper credit is not given to earlier works on the subject

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

characterizing filtered light waves corrupted by phase noise the phase noise associated with single mode semiconductor lasers must be accounted for in performance studies of lightwave communication systems the standard phase noise model is a brownian motion stochastic process although many analyses of lightwave communication systems have been published none to the authors knowledge has fully adhered to the standard model the reason is that a proper characterization of filtered lightwave signal had not been achieved such a characterization along with theoretical approaches to obtaining it is detailed the authors show for example how to generate probability density functions pdfs of the magnitude of a filtered laser tone with special attention to the tail region and how to analytically represent the characteristic function of the pdf in closed form in the small phase noise realm with the characterization in place the stage is now set for determining the bit error rate performance of advanced detection techniques which seek to mitigate the phase noise impairment

on fuzzy approximately cubic type mapping in fuzzy banach spaces abstract the first study of the fuzzy approximately cubic mappings in nonlinear analysis is due to mirmostafaee and moslehian 2008 and a fuzzy version of a generalized hyers ulam rassias type stability for the cubic functional equation in the fuzzy normed linear space setting is presented in this note we give an alternative proof of this result using the fixed point method in probabilistic metric spaces moreover we investigate fuzzy generalized hyers ulam rassias stability of an n dimensional cubic type functional equation in fuzzy banach spaces

fuzzy stability of the jensen functional equation we establish a generalized hyers ulam rassias stability theorem in the fuzzy sense in particular we introduce the notion of fuzzy approximate jensen mapping and prove that if a fuzzy approximate jensen mapping is continuous at a point then we can approximate it by an everywhere continuous jensen mapping as a fuzzy version of a theorem of schwaiger we also show that if every fuzzy approximate jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping then the fuzzy norm is complete

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

stability of additive mappings in non archimedean fuzzy normed spaces in this paper we introduce a notion of a non archimedean fuzzy norm and study the stability of the cauchy equation in the context of non archimedean fuzzy spaces in the spirit of hyers ulam rassias gavruta as a corollary the stability of the jensen equation is established we indeed present an interdisciplinary relation between the theory of fuzzy spaces the theory of non archimedean spaces and the theory of functional equations

the equivalence of convergences of sequences of fuzzy numbers and its applications to the characterization of compact sets in this paper with the help of the convergence of sequences of fuzzy numbers with respect to the lebesgue measure we study the relationship between convergences of sequences of fuzzy numbers with respect to the endograph metric the sendograph metric and the l p metric we prove that these convergences are equivalent under proper conditions in addition by applying our result we give a new characterization of compact sets in fuzzy number space with the sendograph metric

graded sets and points a stratified approach to fuzzy sets and points abstract in this paper we define the concepts of graded set and graded point as well as the usual theoretical set operations and relations and the extension of mappings between graded sets these definitions provide a method to extend concepts of classical set theory this method is related to fuzzy set theory and generalizes some properties of the family of cuts moreover the graded points verify the following two properties which cannot happen with fuzzy points

on the evolution of harmonic maps in higher dimensions on etablit des resultats de regularite partielle et l existence de solutions regulieres globales pour le probleme d evolution pour des applications harmoniques avec des donnees petites

simplification of erceg s fuzzy metric function and its application abstract in this paper we greatly simplify the definition of erceg s p q p metric on a fuzzy lattice l on the basis of this a new pointwise p q p metric is introduced being defined on the set of all non zero join irreducible elements of a fuzzy lattice l meanwhile we prove that it can be directly extended to erceg s p q p metric defined on the fuzzy lattice l these results are exactly what erceg wanted to obtain furthermore we investigate the application of the pointwise metric to fuzzy p metric spaces

the regularity of harmonic maps into spheres and applications to bernstein problems we show the regularity of and derive a priori estimates for weakly harmonic maps from a riemannian manifold into a euclidean sphere under the assumption that the image avoids some neighborhood of a half equator the proofs combine constructions of strictly convex functions and the regularity theory of quasilinear elliptic systems we apply these results to the spherical and euclidean bernstein problems for minimal hypersurfaces obtaining new conditions under which compact minimal hypersurfaces in spheres or complete minimal hypersurfaces in euclidean spaces are trivial

fuzzy normed space of operators and its completeness in this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced and the boundedness of such an operator is described furthermore the space of all bounded linear operators endowed with this fuzzy norm is studied consequently its topological structure as well as completeness is given and that it can itself be made into a fuzzy normed linear space is also shown

condensing operators and topological degree theory in standard fuzzy normed spaces in this paper level cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied using the extensions of nonlinear compact operators topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces as an application of degree theory a fixed point theorem for condensing operators is presented

an asymptotic expression for the information and capacity of a multidimensional channel with weak input signals an asymptotic expression is derived for the shannon mutual information between the input and output signals for a relatively large class of continuous alphabet memoryless channels in the case of weak input signals when the input space is multidimensional the authors extend a result of ibragimov and khas minskii 1972 from the one dimensional to the n dimensional case the asymptotic expression obtained relates the shannon 1948 mutual information function and the fisher information matrix this expression is used to derive an asymptotic expression for the capacity of continuous alphabet memoryless channels with vector valued weak input signals this asymptotic capacity involves the largest eigenvalue of the fisher information matrix evaluated at the zero input signal

fixed point theorems on fuzzy normed linear spaces in this paper definitions of strongly fuzzy convergent sequence l fuzzy weakly convergent sequence and l fuzzy weakly compact set are given in a fuzzy normed linear space the concepts of fuzzy normal structure fuzzy non expansive mapping uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non expansive mappings are proved