sampling and interpolation in large bergman and fock spaces we obtain sampling and interpolation theorems in weighted spaces of analytic functions for radial weights of arbitrary more rapid than polynomial growth we give an application to invariant subspaces of arbitrary index in large weighted bergman spaces

iterative approaches to convex feasibility problems in banach spaces abstract the convex feasibility problem cfp of finding a point in the nonempty intersection i 1 n c i is considered where n 1 is an integer and each c i is assumed to be the fixed point set of a nonexpansive mapping t i x x with x a banach space it is shown that the iterative scheme x n 1 n 1 y 1 n 1 t n 1 x n is strongly convergent to a solution of cfp provided the banach space x either is uniformly smooth or is reflexive and has a weakly continuous duality map and provided the sequence n satisfies certain conditions the limit of x n is located as q y where q is the sunny nonexpansive retraction from x onto the common fixed point set of the t i s

a change of subscripts of the stimulus placements for a four point sampling method because the variance parameter in a cumulative normal function is not the same as the spread parameter s of a logistic function the subscripts of the four stimulus placements of eq 3 and thereafter of lam et al j acoust soc am 99 3689 3693 1996 should be x12 x27 x73 and x88

convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive banach spaces let e be a real reflexive banach space with a uniformly g teaux differentiable norm let k be a nonempty closed convex subset of e suppose that every nonempty closed convex bounded subset of k has the fixed point property for nonexpansive mappings let t1 t2 tn be a family of nonexpansive self mappings of k with f i 1nfix ti 0 f fix tntn 1 t1 fix t1tn t2 fix tn 1tn 2 t1tn let n be a sequence in 0 1 satisfying the following conditions c1 lim n 0 c2 n for a fixed 0 1 define sn k k by snx 1 x tnx x k where tn tnmodn for an arbitrary fixed u x0 k let b x k tntn 1 t1x x 1 u for some 1 be bounded and let the sequence xn be defined iteratively by xn 1 n 1u 1 n 1 sn 1xn for n 0 assume that limn tnxn tn 1xn 0 then xn converges strongly to a common fixed point of the family t1 t2 tn this convergence theorem is also proved for non self maps

approximation methods for common fixed points for a countable family of nonexpansive mappings abstract let e l p or l p space 1 p let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i i 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that the iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b e l p 1 p and at least one of the maps t i s is demicompact our theorems extend the results of p mainge approximation methods for common fixed points of nonexpansive mappings in hilbert space j math anal appl 325 2007 469 479 from hilbert spaces to l p spaces 1 p

a general iterative method for an infinite family of nonexpansive mappings abstract let h be a real hilbert space consider the iterative sequence x n 1 n f x n n x n 1 n i n a w n x n where 0 is some constant f h h is a given contractive mapping a is a strongly positive bounded linear operator on h and w n is the w mapping generated by an infinite countable family of nonexpansive mappings t 1 t 2 t n and 1 2 n such that the common fixed points set f n 1 fix t n 0 under very mild conditions on the parameters we prove that x n converges strongly to p f where p is the unique solution in f of the following variational inequality a f p p x 0 for all x f which is the optimality condition for the minimization problem min x f 1 2 a x x h x

a logistic prediction model for individual allowable noise levels annoyance to noise is probably a good measure of the potential for complaint and community action each individual s degree of annoyance to noise cannot be accurately predicted from conventional laboratory studies and social surveys therefore a logistic prediction model for individual allowable noise levels has been developed in a previous paper k furihata et al acta acust acust 93 73 83 2007 an annoyance scale using the most frequently used annoyance ratings related to noise for community noise assessment in japan was constructed the dose response relationships were obtained by actually listening to sounds in a field situation 1474 subjects carried out at 14 metropolitan cities in japan the logistic prediction model was developed using the logistic regression parameters estimated from each cumulative percentage curve of seven annoyance scale scores based on all data n 2940 to verify the hypothesis individual relationships between annoyance and laeq 5min for 24 normal hearing subje

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

an iterative method for finding common solutions of equilibrium and fixed point problems we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem

a comparison of threshold estimation methods in children 6 11 years of age estimating detection threshold for auditory stimuli in children can be problematic because of lapses in attention and the time limits usually imposed by scheduling restrictions or fatigue data reported here were collected to compare the stability of threshold estimation procedures in testing children ages 6 to 11 in a three alternative forced choice paradigm stimuli consisted of a 1 khz tonal signal and a gaussian noise masker bandpass filtered between 500 2000 hz and presented at 25 db spectrum level the signal was either presented for 400 ms in the presence of a continuous masker simultaneous masking or for 10 ms just prior to a 400 ms masker backward masking for each masking paradigm the 79 correct threshold was assessed via each of three procedures 3 down 1 up adaptive staircase levitt maximum likelihood estimation mle and method of constant stimuli percent correct was measured at the end of the study for a signal 10 db above the previously determined threshold in order to estimate the most appropriate psychometric function asymptote for fitting data collected via the method of constant stimuli both the mle and levitt procedures produced equally stable threshold estimates for both conditions and age groups this was the case despite considerable variability in backward masking thresholds

determination of optimal data placement for psychometric function estimation a computer simulation psychometric functions are used to relate the responses of a subject to physical stimuli in a variety of psychophysical tasks however it is time consuming to obtain data to determine a psychometric function if many stimulus levels and many trials are required a computer simulation was conducted to determine the minimum number of data points needed for such a determination the computer simulation also determined the optimal placements of the stimuli and the number of trials per datum point for psychometric function determinations results indicate that a 2 point sampling method with 30 50 trials per point at optimal locations can produce a psychometric function with accurate spread and threshold estimates in a yes no paradigm however the 4 point sampling method yields statistically smaller variances of the estimates for the 2 alternative forced choice paradigm at least 120 trials per point are needed for the 2 point sampling method s estimated parameters to differ from the known parameter values by less than 5 the simulation results suggest that 3 alternative or 4 alternative forced choice is preferable to 2 alternative furthermore when a criterion free paradigm is not required the yes no paradigm is a better procedure than m alternative forced choice for obtaining the corresponding psychometric function because of smaller standard deviation of the estimates and smaller number of trials point required

estimating parameters for psychometric functions using the four point sampling method although a psychometric function describing a subject s responses to some physical stimuli is of considerable value characterizing such functions is time consuming and hence is not carried out routinely in psychophysical experiments a principal reason for the lack of efficiency in characterizing a psychometric function is the use of sampling methods that either converge on a single point on the psychometric function such as the pest method or which distribute observations uniformly over a wide range such as the constant stimuli method as an alternative a multimodal four point sampling method has been proposed c f lam j h mills and j r dubno j acoust soc am 99 3689 3693 1996 a psychometric function is then fitted to the four points each with several trials to estimate the threshold and slope parameters of the psychometric function adaptive methods such as the up down methods h levitt j acoust soc am 49 467 477 1971 can be used to provide good initial estimates of the threshold and spread parameters of a psychometric function described by a logistic function in ongoing studies of age related changes in auditory masking and discrimination this new four point sampling method has been applied to determine psychometric functions for absolute thresholds as a function of duration thresholds in simultaneous and forward masking frequency discrimination and intensity discrimination in both young and aged human subjects results indicate that a reduction in data collection time of about 50 with no increase in variance can be achieved this increase in efficiency applies to simple detection tasks by normal hearing subjects as well as to complex discrimination tasks by older subjects with hearing loss

approximation methods for common fixed points of nonexpansive mappings in hilbert spaces abstract the aim of this work is to propose implicit and explicit viscosity like methods for finding specific common fixed points of infinite countable families of nonexpansive self mappings in hilbert spaces two numerical approaches to solving this problem are considered an implicit anchor like algorithm and a nonimplicit one the considered methods appear to be of practical interests from the numerical point of view and strong convergence results are proved

a general iterative method for a finite family of nonexpansive mappings abstract we study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity also we show that the convergence of the proposed algorithm can be proved under some types of control conditions

a maximum likelihood method for estimating thresholds in a yes no task a maximum likelihood procedure for estimating threshold values in a yes no task is presented in computer simulations of this procedure it is demonstrated that the variability of the threshold estimates is little affected by the density of the hypotheses tested for a fixed range or by serious misestimates of the slope of the psychometric functions the threshold value is also largely independent of the starting value of the signal the standard deviation of the threshold estimates appears to decrease with the square root of the number of trials with a 2 to 3 db standard deviation possible if only 12 trials are used in the threshold estimates data are presented using human listeners tested on 5 days two threshold estimates based on 12 trials were made at each of the six audiometric frequencies on each day the mean data appear sensible and the standard deviation of the measured thresholds is about 3 db using this procedure it takes less than 3 min to measure the audiogram for a single ear

iterative approaches to common fixed points of nonexpansive mappings in banach spaces abstract the iteration scheme for families of nonexpansive mappings essentially due to halpern bull amer math soc 73 1967 957 961 is established in a banach space the main theorem extends a recent result of o hara et al nonlinear anal 54 2003 1417 1426 to a banach space setting for the same iteration scheme with finitely many mappings a complementary result to a result of jung and kim bull korean math soc 34 1997 93 102 also bauschke j math anal appl 202 1996 150 159 is obtained by imposing other condition on the sequence of parameters our results also improve results in c r acad sci ser a b paris 284 1977 1357 1359 j math anal appl 211 1997 71 83 arch math 59 1992 486 491 in framework of a hilbert space

iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces abstract let e be a uniformly convex real banach space with a uniformly g teaux differentiable norm let k be a closed convex and nonempty subset of e let t i i 1 be a family of nonexpansive self mappings of k for arbitrary fixed 0 1 define a family of nonexpansive maps s i n 1 by s i 1 i t i where i is the identity map of k let f i 1 f t i 0 it is proved that an iterative sequence x n defined by x 0 k x n 1 n u i 1 i t n s i x n n 0 converges strongly to a common fixed point of the family t i i 1 where n and i t n are sequences in 0 1 satisfying appropriate conditions in each of the following cases a e l p 1 p and b at least one of the t i s is demicompact

embedding theorems and integration operators on bergman spaces with rapidly decreasing weights we completely describe those positive borel measures in the unit disc d such that the bergman space ap w lq 0 0 and some double exponential type weights as an application of that result we characterize the boundedness and the compactness of tg ap w aq w 0 p q w w where tg is the integration operator tgf z 0zf g d the particular choice of the weight w r answers an open question posed by a aleman and a siskakis we also describe those analytic functions in d for which tg belongs to the schatten p class of a2 w 0 p

strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive banach spaces in this paper by using some new analysis techniques we study the approximation problems of common fixed points of halpern s iterative sequence for a class of finite nonexpansive mappings in strictly convex and reflexive banach spaces by using banach s limit the main results presented in this paper generalize extend and improve the corresponding results of bauschke the approximation of fixed points of compositions of nonexpansive mappings in hilbert spaces j math anal appl 202 1996 150 159 halpern fixed points of nonexpansive maps bull am math soc 73 1967 957 961 shioji and takahashi strong convergence of approximated sequences for nonexpansive mappings in banach spaces proc am math soc 125 1997 3641 3645 takahashi et al approximation of common fixed points of a family of finite nonexpansive mappings in banach spaces sci math jpn 56 2002 475 480 wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 xu another control condition in an iterative method for nonexpansive mappings bull austral math soc 65 2002 109 113 remarks on an iterative method for nonexpansive mappings commun appl nonlinear anal 10 2003 67 75 and others

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

pointwise estimates of weighted bergman kernels in several complex variables abstract we prove new pointwise bounds for weighted bergman kernels in c n whenever a coercivity condition is satisfied by the associated weighted kohn laplacian on 0 1 forms our results extend the ones obtained by christ in 5 our main idea is to develop a version of agmon theory originally introduced in 1 to deal with schrodinger operators for weighted kohn laplacians on 0 1 forms inspired by the fact that these are unitarily equivalent to certain generalized schrodinger operators

compact differences of composition operators on large weighted bergman spaces abstract while there have been extensive studies regarding the theory of composition operators in standard bergman spaces there have not been many results pertaining to large bergman spaces due to a lack of useful tools in this paper we obtain a complete characterization of the compact differences of composition operators in bergman spaces with weight of z e 1 1 z using a newly defined riemannian distance moreover we discuss the compact differences of composition operators in bergman spaces with general weights

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem