the dominguez lorenzo condition and multivalued nonexpansive mappings abstract let e be a nonempty bounded closed convex separable subset of a reflexive banach space x which satisfies the dominguez lorenzo condition i e an inequality concerning the asymptotic radius of a sequence and the chebyshev radius of its asymptotic center we prove that a multivalued nonexpansive mapping t e 2 x which is compact convex valued and such that t e is bounded and satisfies an inwardness condition has a fixed point as a consequence we obtain a fixed point theorem for multivalued nonexpansive mappings in uniformly nonsquare banach spaces which satisfy the property worth extending a known result for the case of nonexpansive single valued mappings we also prove a common fixed point theorem for two nonexpansive commuting mappings t e e and t e kc e where kc e denotes the class of all compact convex subsets of e when x is a uniformly convex banach space

fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions abstract let x be a banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict opial condition let c be a bounded closed convex subset of x kc x the family of all compact convex subsets of x and t a nonexpansive mapping from c into kc x with bounded range we prove that t has a fixed point the nonstrict opial condition can be removed if in addition t is an 1 contractive mapping

edelstein s method and fixed point theorems for some generalized nonexpansive mappings abstract a new condition for mappings called condition c which is more general than nonexpansiveness was recently introduced by suzuki t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 following the idea of kirk and massa theorem in w a kirk s massa remarks on asymptotic and chebyshev centers houston j math 16 1990 364 375 we prove a fixed point theorem for mappings with condition c on a banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact this covers a result obtained by suzuki t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 we also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of banach spaces satisfying property d consequently we extend the results in t suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 to many other banach spaces

the jordan von neumann constants and fixed points for multivalued nonexpansive mappings the purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of banach spaces furthermore we demonstrate a relationship between the weakly convergent sequence coefficient wcs x and the jordan von neumann constant cnj x of a banach space x using this fact we prove that if cnj x is less than an appropriate positive number then every multivalued nonexpansive mapping t e kc e has a fixed point where e is a nonempty weakly compact convex subset of a banach space x and kc e is the class of all nonempty compact convex subsets of e

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

spatial antialias filtering in the slowness frequency domain a rigorous explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first nyquist wavenumber and aliased energy that is folded back across the nyquist in the horizontal slowness frequency domain the spatial filtering in the slowness frequency domain is explicit free from any event linearity assumption and does not require any interpolation the spatially aliased energy is dispersive and present at small and large slownesses comparison of the output data after antialias spatial filtering with output data after conventional antialias frequency filtering shows that the filter removes the spatially aliased frequencies selectively at each slowness antialias low pass frequency filtering under or overcorrects for spatial aliasing at all slownesses a seismic gather can be spatially dealiased only at the expense of wavelet spectral changes dealiasing and preservation of amplitude variations with offset are not simultaneously possible

sampling aliasing and inverting the linear radon transform sampling a signal too slowly results in temporal frequency aliasing sampling a wave too infrequently in space causes spatial aliasing slowness aliasing is another problem that can occur in some cases even when temporal and spatial frequency aliasing are absent as its name suggests slowness aliasing can cause a wave with one value of slowness to be interpreted as a wave with a different value of slowness for a 2d signal or an image the penalty of undersampling is that we may misrepresent both the spatial frequency and the orientation of the pattern if the pattern is moving then the direction of motion may also be misrepresented the linear radon transform deans 1983 or the related slope intercept form durrani and bisset 1984 is a useful tool to analyze seismic data foster and mosher 1992 dunne and beresford 1995 although sampling and aliasing are two recurring problems turner 1990 marfurt et al 1996 bardan 1998 on the other hand in the optical literature fowles 1989 the effect of fraunhofer diffraction indicates what is happening when a grating is illuminated by a monochromatic plane wave this paper demonstrates how sampling and inverting of the linear radon transform is related to fraunhofer diffraction patterns

wavelet radon domain dealiasing and interpolation of seismic data spatial aliasing is unavoidable in some seismic data and has serious effects on the performance of multichannel data processing and migration antialias filtering produces distortion of the signal through the removal of high frequency information in contrast dealiasing produces an unaliased estimate of the signal at all frequencies present in the original time series a new dealiasing algorithm is developed by exploiting the properties of seismic wavefields in the wavelet radon transform domain specifically the overlap of information between wavelet scales at the same frequency the effectiveness of the wavelet radon dealiasing algorithm is demonstrated through the processing of both synthetic and field seismic data

extremal structure of the unit ball of direct sums of banach spaces abstract we characterize the extreme points and smooth points of the unit ball of certain direct sums of banach spaces we use these results to characterize noncreasiness and uniform noncreasiness of direct sums thereby extending results of the second author s saejung extreme points smooth points and noncreasiness of direct sum of banach spaces nonlinear anal 67 2007 1649 1653

remarks on sufficient conditions for fixed points of multivalued nonexpansive mappings abstract in recent papers s dhompongsa t dominguez benavides a kaewcharoen a kaewkhao b panyanak the jordan von neumann constants and fixed points for multivalued nonexpansive mappings j math anal appl 320 2006 916 927 s dhompongsa a kaewcharoen a kaewkhao the dominguez lorenzo condition and multivalued nonexpansive mappings nonlinear anal 64 2006 958 970 two sufficient conditions namely the dominguez lorenzo condition and property d for fixed points of multivalued nonexpansive mappings are introduced the authors also give some sufficient conditions for the dominguez lorenzo condition and property d in their proofs it seems reasonable to use the james and von neumann jordan constants with slight modifications significant improvements are obtained some new estimates are tight in hilbert spaces

the james constant the jordan von neumann constant weak orthogonality and fixed points for multivalued mappings abstract we give some sufficient conditions for the dominguez lorenzo condition in terms of the james constant the jordan von neumann constant and the coefficient of weak orthogonality as a consequence we obtain fixed point theorems for multivalued nonexpansive mappings

two different approaches for iris recognition using gabor filters and multiscale zero crossing representation abstract importance of biometric user identification is increasing everyday one of the most promising techniques is the one based on the human iris the authors in this work describe different approaches to develop this biometric technique based on the works carried out by daugman the authors have worked using gabor filters and hamming distance but in addition they have also worked in zero crossing representation of the dyadic wavelet transform applied to two different iris signatures one based on a single virtual circle of the iris the other one based on an annular region also other metrics have been applied to be compared with the results obtained with the hamming distance in this work euclidean distance and d z will be shown the last proposed approach is translation rotation and scale invariant results will show a classification success up to 99 6 achieving an equal error rate down to 0 12 and the possibility of having null false acceptance rates with very low false rejection rates

cyclic mathematical morphology in polar logarithmic representation we propose in this paper to perform mathematical morphology operators in a geometric transformation of an image as a result of this procedure processing images with regular structuring elements in the transformed domain is equivalent to working with deformed structuring elements in the original representation more specifically the conversion into polar logarithmic coordinates provides satisfying results in image analysis applied to round objects if they are roughly origin centered we have illustrated the interest of the derived cyclic morphology with two pattern recognition examples erythrocyte shape analysis and multiscale description of iris textures

the fixed point property for multivalued nonexpansive mappings we show some properties concerning geometrical constants of banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties

lim s theorems for multivalued mappings in cat 0 spaces let x be a complete cat 0 space we prove that if e is a nonempty bounded closed convex subset of x and t e k x a nonexpansive mapping satisfying the weakly inward condition i e there exists p e such that p 1 tx ie x x e 0 1 then t has a fixed point in banach spaces this is a result of lim on asymptotic centers and fixed points of nonexpansive mappings canad j math 32 1980 421 430 the related result for unbounded r trees is given

parabolic radon transform sampling and efficiency a good choice of the sampling in the transform domain is essential for a successful application of the parabolic radon transform the parabolic radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform fourier transform this leads to new and useful insights in the parabolic radon transform using nonuniform fourier theory we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general irregular sampling a significantly smaller sampling interval requires stabilization if diagonal stabilization is used no gain in resolution is obtained in contrast to conventional implementations the curvature sampling interval is proposed to be inversely proportional to the temporal frequency this results in improved quality of the transform and yields significant savings in computation time

banach space properties sufficient for normal structure in this paper we establish lower bounds for the weakly convergent sequence coefficient wcs x of a banach space x in terms of some well known moduli and coefficients by mean of these bounds we identify several properties of geometrical nature which imply normal structure we show that these properties are strictly more general than other previously known sufficient conditions for normal structure

banach ultrapowers and multivalued nonexpansive mappings the banach ultrapower construction is applied in fixed point theory for multivalued mappings we introduce the notion of ultra asymptotic centers and use it to remove the separability assumption from the results of dominguez benavides lorenzo ramirez 2004 and dhompongsa kaewcharoen kaewkhao 2006

some geometric conditions which imply the fixed point property for multivalued nonexpansive mappings abstract we show some geometric conditions on a banach space x concerning the modulus of smoothness the coefficient of weak orthogonality the coefficient r a x the james constant and the jordan von neumann constant which imply the existence of fixed points for multivalued nonexpansive mappings these fixed point theorems improve some previous results and give affirmative answers to some open questions

pitfalls of using conventional and discrete radon transforms on poorly sampled data the least square discrete radon transform drt is currently one of the most popular methods used in the suppression of multiples and other coherent noise events on irregularly sampled data gathers used for prestack true amplitude analysis unfortunately in the absence of a priori information this technique suffers from the same aliasing problems as fourier and conventional p methods although the drt is able to reconstruct the original image more accurately than conventional p transforms a harmful by product is an increase in the amplitude of aliased events in the transform domain in particular the drt will boost the amplitude of the aliases of true events that fall outside the p analysis window to help reconstruct the input data these amplified aliases degrade signal periodicity in the p domain if muted they can destroy subtle amplitude changes necessary for amplitude variation with offset avo analysis at the very least one should carefully evaluate the choice of analysis wind

geodesic methods in quantitative image analysis abstract let x be a part of an image to be analysed given two arbitrary points x and y of x let us define the number d x x y as follows d x x y is the lower bound of the lengths of the arcs in x ending at points x and y if such arcs exist and if not the function d x is an x intrinsic distance function called geodesic distance note that if x and y belong to two disjoint connected components of x d x x y in other words d x seems to be an appropriate distance function to deal with connectivity problems in the metric space x d x all the classical morphological transformations dilation erosion skeletonization etc can be defined the geodesic distance d x also provides rigorous definitions of topological transformations which can be performed by automatic image analysers with the help of parallel iterative algorithms all these notions are illustrated by several examples definition of the length of a fibre and of an effective length factor automatic detection of cells having at least one nucleus or having one single nucleus definitions of the geodesic center and of the ends of an object without a hole etc the corresponding algorithms are described