taylor s theorem for analytic functions

... function-theoretic result known as Julia s lemma In case ϕ has a fixed point, but is not the identity or an elliptic disk automorphism, one can use Schwarz s lemma in classical complex analysis to show that ... MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Florida, 1995 J B Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, vol 96, ... (2.8) is satisfied for some finite set of points in U if and only if T= z∈U\{ω} Γz,ϕ(z) , (2.10) which is a direct consequence of the compactness of T Thus, arguing by contradiction, one should assume...

Ngày tải lên: 23/06/2014, 00:20

... ,n, Fα1 ,α2 , ,αn ,β (z) becomes the integral operator Fα,β (z) considered in [6] Main results Theorem 2.1 Let M ≥ and the functions fi ∈ Ꮽ, for i ∈ {1, ,n}, satisfy the condition (1.4), and let ... 1/β 1/α fi (t) t dt (2.13) is in the class ᏿ Proof In Theorem 2.1, we consider α1 = α2 = · · · = αn = α Corollary 2.3 Let the functions fi ∈ Ꮽ, for i ∈ {1, ,n}, satisfy the condition (1.4), and ... (z) (2.11) So from (2.1), we have c|z|2β + − |z|2β Applying Theorem 1.1, we obtain that Fα1 ,α2 , ,αn ,β is univalent Theorem 2.2 Let M ≥ and the functions fi ∈ Ꮽ, for i ∈ {1, ,n} satisfy the condition...

Ngày tải lên: 21/06/2014, 22:20

... p0 s1 − p0 s2 ≤ A , ln1/ s1 − s2 s1 − s2 ≤ , s1 ,s2 ∈ [0, ] (2.11) Since |t (s1 ) − t (s2 )| ≤ |s1 − s2 |, condition (2.10) always implies (2.11) Inversely, (2.11) implies (2.10) if, for instance, ... obtain similar estimates by the same way as in case D+ As to δ ≤ it is necessary to consider two cases: < r < r0 and r0 < r < for some fixed r0 In the last case the appropriate estimates can ... (Lyapunov curves) and G is in a sufficiently wide class of bounded measurable functions, or (II) Γ belongs to a wide class of curves but G is in a more narrow class than in the previous case In situation...

Ngày tải lên: 23/06/2014, 00:20

... combinatorics 17 (2010), #R34 Recall that the algebra Sym of noncommutative symmetric functions is the free associative algebra, on the symbol set Sn , whose basis is given by S I = Si1 · · · Sin for ... Jumadildayeva for assistance in making calculations, and to the anonymous referee for essential remarks References [1] A Bjărner, M.L Wachs, Permutation Statsitics and Linear extensions of posets, J o ... iff Des(I) ⊆ Des(J) In this case we say that I is coarser than J The descent composition I = C(σ) of a permutation σ ∈ Sn is the composition of n whose descents are exactly the set of descent...

Ngày tải lên: 08/08/2014, 12:22

... Operators on Spaces of Univalent Functions Publishing House of the Romanian Academy of Sciences, Bucharest (in Romanian) (2004) Darus, M, Faisal, I: A study on Becker s univalence criteria Abstr ... ∀i Then, the family of functions f denoted by Gn,a belong to the class S If we substitute n = and M = n = in Theorem 2.4, we get the results of Corollaries 3.1 and 3.2, respectively Other work ... The first author is currently a PhD student under supervision of the second author and jointly worked on the results All authors read and approved the final manuscript Competing interests The...

Ngày tải lên: 20/06/2014, 22:20

... object of the present paper is to consider some generalized conditions for functions f(z) to be in the classes S ∗ or K Generalized conditions for starlikeness We begin with the statement and the ... Lemma 1.3 This means that if f(z) satisfies |f (z)| N3 √ − |f (0)| (z ∈ U), (2:6) then f (z) ∈ S ∗ Thus, the theorem is holds true for j = Next, we suppose that the theorem is true for j = 2, 3, 4, ... Published: 17 October 2011 References Nunokawa, M: On the order of strongly starlikeness of strongly convex functions Proc Jpn Acad 68, 234–237 (1993) Mocanu, PT: Some starlikeness conditions for...

Ngày tải lên: 20/06/2014, 22:20

... economy See for a nice survey Notations and Basic Concepts Throughout this paper, the standard notations and terminologies in nonlinear analysis are used see the papers by Kirk and Sims , Granas and ... Mathematics, vol 30, pp 475– 488, 1969 31 N S Papageorgiou, “Convergence theorems for fixed points of multifunctions and solutions of differential inclusions in Banach spaces,” Glasnik Matematiˇ ki Serija ... well-posedness concept introduced in 35 ´ c Remark 3.7 An open question is to present a theory of the Ciri´ -type multivalued contraction theorem see 36 For some problems for other classes of...

Ngày tải lên: 21/06/2014, 11:20

... restriction putted there ν > dim Γ/m implies that of this paper Applications In this last section, we will briefly discuss two particular cases which arise when considering 3.17 Case It is easily ... Euclidean space m is even whence we will put m 2n from now on In a series of recent papers, so-called isotonic Clifford analysis has emerged as yet a refinement of the standard case but also has strong ... converges Note that this is in agreement with 12 for Γ to be d-summable Observe that a d-summable surface has box dimension dim Γ ≤ d Meanwhile, if Γ has box dimension less than d, then Γ is d-summable...

Ngày tải lên: 21/06/2014, 18:20

... proof, see 2, page 71 or 1, page 53 A class of functions which is between the class of convex functions and the class of Jensen-convex functions is the class of Wright-convex functions A function ... Inequalities and Applications holds for every x, y ∈ I It is clear that every convex function is Jensen-convex To see that the class of convex functions is a proper subclass of Jensen-convex functions, ... assumptions for 1.1 is relaxing the assumption of positivity of weights pi , i 1, , n The most important result in this direction is the JensenSteffensen inequality see, e.g., 1, page 57 which states...

Ngày tải lên: 22/06/2014, 02:20

... function f for various unknown weight vectors p This is why the statement of Theorem 1.2 makes the assumption that this is true for all possible weight vectors The following lemma gives a simple sufficient ... where θ1 is as given in Theorem 1.2 Proof It suffices to show For the case n 2, as before, write x2 t x1 , The case of n is trivial, since σ where ≤ t ≤ b − x1 /x1 , p1 − q, and p2 q With these, we ... can choose any θ1 satisfying ≤ θ1 ≤ μ1 For n > 2, let us suppose that 1.3 has been proved for up to n − 1, and consider the case of n Fix x1 , , xn We may assume that all xk are distinct...

Ngày tải lên: 22/06/2014, 03:20

... will be established Hence, it is possible to construct the lower and the upper bounds for Kε Proofs of the main results and some auxiliary results In Sections 3.1 and 3.2 we discuss, present, and ... fact this was our original interest in the subject The paper is organized as follows In Section 2, we present and discuss our main results In Section 3, these results are proved via some auxiliary ... a set diameter εδ(ε) contained in a ball of radius δ(ε) Here we assume that δ(ε) = o(εn−2 ) as ε→0 Also we suppose that Γε = Γε ∪ S In this case our main result reads as follows Theorem 2.3 Suppose...

Ngày tải lên: 22/06/2014, 11:20

... > 0;γ > −1) was introduced by Choi et al [2], who investigated (among other things) several inclusion properties involving various subclasses of analytic and univalent functions For γ = n(n ∈ ... the classes ᏿λ,α1 (q ,s; η;φ), ᏷λ,α1 (q ,s; η;φ), and Ꮿλ,α1 (q ,s; η,β;φ,ψ) associated with the operator Hλ,q ,s (α1 ) Some applications involving integral operators are also considered Inclusion Properties ... starlike functions, ” Annales Universitatis Mariae Curie-Skłodowska, Sectio A, vol 45, pp 89–97, 1991 [4] J Dziok and H M Srivastava, “Classes of analytic functions associated with the generalized...

Ngày tải lên: 22/06/2014, 18:20

Ngày tải lên: 05/08/2014, 15:20

... approximate extensions, has been used by Dinh et al [10] to derive a series of subdifferential calculus rules, different generalizations of Farkas lemma for non-necessarily convex systems, optimality ... extension, even in a finite dimensional setting’ In order to overcome this difficulty and achieve a result easier to use in applications, we address, in very much the same spirit as the ε-strategies ... if is also dominated by p ∗∗ On this ground, we address the class of ph -functions with the V -approximate extension property in the setting of a Hausdorff locally convex space X : Proposition...

Ngày tải lên: 16/12/2017, 05:43

... fiber Sfx ;x Then, it is clear that Sf;x D Sfx ;x 3.2 Integral of a gauge form and volume Poincaré series Stft formal schemes Assume that X is a separated generically smooth formal kŒŒt scheme ... by formal functions f and g, respectively (Theorem 3.4) This is proved in Section using the development of tools in Section as well as some analogous techniques in the proof of the regular version ... local form of Denef–Loeser s and Looijenga s motivic Thom–Sebastiani theorem is included (Theorem 2.1), using the main references [3–7] and [19] The local form states that Sf ˚g;.x;y/ D Sf;x Sg;y...

Ngày tải lên: 16/12/2017, 15:10

... Kidney Diseases (NIDDK) fact sheet Vascular Access for Hemodialysis Who Performs It Hemodialysis is usually done in a dialysis center by nurses and trained technicians In some parts of the country, ... there is adequate time—usually from 10 days to or weeks for the insertion site to heal This is another way in which planning your dialysis access can improve treatment success This catheter stays ... these drugs may also cause liver or kidney damage in a few patients Diet for Transplantation Diet for transplant patients is less limited than it is for dialysis patients, although you may still...

Ngày tải lên: 01/09/2012, 11:09

... PRESS Most Washington Square Press Books are available at special quantity discounts for bulk purchases for sales promotions, premiums or fund raising Special books or book excerpts can also be ... Konzentrationslager This translation first published by Beacon Press in 1959 Beacon Press books are published under the auspices of the Unitarian Universalist Association A Washington Square Press Publication ... these distressing disorders in the anxiety caused by conflicting and unconscious motives Frankl distinguishes several forms of neurosis, and traces some of them (the noögenic neuroses) to the...

Ngày tải lên: 07/11/2012, 14:03

... for assessment is necessary Among the various criteria and models for translation quality assessment, House s model is chosen in this study because it is deemed to have a comprehensive set of ... different views on equivalence will be discussed but there shall be no separate discussion of translation assessment; instead, it is implied that assessment of a translation is based on the respective ... has been translated into English by several translators An assessment of the English version of this law is thus desirable 2 Significance of the study The results of this study will help test...

Ngày tải lên: 07/11/2012, 14:36

... and answer: 1/ What you usually at recess? 2/ Do you usually talk with your friends at recess? 3/ What you usually after school? In groups, describe a recess of your school • Time • Students’ feeling ... English class today? Today we have English class at … Number What you often after school? Number Are you interested in learning English? Why? Number What you study in Literature class? We study ... the answer: Which activity is the most popular activity at recess? Talking What is the boy doing? He is playing blindman s bluff What are the girls doing? They are skipping rope In pairs, ask...

Ngày tải lên: 29/09/2013, 08:10

... and I ! = 0, this doesn’t really tell us anything useful about I Thus, P P we consider subsets of , rather than individual elements of e Distribution of B T  If is constant, then n o Z ... is a martingale under IP 192 Lemma 1.54 (Baye s Rule) If X is F t-measurable and  s  t  T , then f IE X jF s = Z s IE XZ tjF s : Proof: It is clear that Z 1s IE XZ tjF s is ... dy (Substitute y = T + b) y = T + b = p 2T ,1 = 0: CHAPTER 17 Girsanov s theorem and the risk-neutral measure 191 fe We can also see that I B T  = by arguing directly from the density formula...

Ngày tải lên: 18/10/2013, 03:20