共查询到20条相似文献,搜索用时 0 毫秒
1.
T. H. Sweetser III 《Journal of Optimization Theory and Applications》1977,23(4):549-562
A set-valued derivative for a function at a point is a set of linear transformations whichapproximates the function near the point. This is stated precisely, and it is shown that, in general, there is not a unique minimal set-valued derivative for functions in the family of closed convex sets of linear transformations. For Lipschitz functions, a construction is given for a specific set-valued derivative, which reduces to the usual derivative when the function is strongly differentiable, and which is shown to be the unique minimal set-valued derivative within a certain subfamily of the family of closed convex sets of linear transformations. It is shown that this constructed set may be larger than Clarke's and Pourciau's set-valued derivatives, but that no irregularity is introduced.The author would like to thank Professor H. Halkin for numerous discussions of the material contained here. 相似文献
2.
Fernando Bombal Ignacio Villanueva 《Journal of Mathematical Analysis and Applications》2008,348(1):444-453
For a holomorphic function f of bounded type on a complex Banach space E, we show that its derivative df:E→E∗ takes bounded sets into certain families of sets if and only if f may be factored in the form f=g○S, where S is in some associated operator ideal, and g is a holomorphic function of bounded type. We also prove that the multilinear and polynomial mappings factor in an analogous way if and only if they are “K-bounded.” 相似文献
3.
S.S. Dragomir 《Applied mathematics and computation》2011,218(3):766-772
Some Hermite-Hadamard’s type inequalities for operator convex functions of selfadjoint operators in Hilbert spaces are given. Applications for particular cases of interest are also provided. 相似文献
4.
T. Tanaka 《Journal of Optimization Theory and Applications》1991,68(2):321-334
It seems that minimax theorems for vector-valued functions found in recent papers have something in common. Taking note of this, we improve several results in the author's recent works and state two types of minimax theorems for vector-valued functions. One theorem refers to functions with some special convexity properties; the other theorem refers to separated functions of the typef(x, y)=u(x)+v(y). The proofs are based on the existence of weak cone saddle points off and on a condition about a pointed convex cone which induces a partial ordering in the image space off. We need the condition (C{0})+clC–C, which implies the Sterna-Karwat condition for a convex coneC of a Hausdorff topological vector space.The author thanks the referees for their valuable suggestions on the original draft. Also, he is grateful to S. Yoshiara for his useful suggestions on the English presentation. 相似文献
5.
Chunlin Lei Degui Yang Xueqin Wang 《Journal of Mathematical Analysis and Applications》2008,341(1):224-234
Let k be a positive integer with k?2; let h(?0) be a holomorphic function which has no simple zeros in D; and let F be a family of meromorphic functions defined in D, all of whose poles are multiple, and all of whose zeros have multiplicity at least k+1. If, for each function f∈F, f(k)(z)≠h(z), then F is normal in D. 相似文献
6.
Hakan Bostanci 《Journal of Mathematical Analysis and Applications》2007,328(1):370-379
In a previous paper M.P. Chen, Z.-R. Wu and Z.-Z. Zou [M.P. Chen, Z.-R. Wu, Z.-Z. Zou, On functions α-starlike with respect to symmetric conjugate points, J. Math. Anal. Appl. 201 (1996) 25-34] developed a method, using some operators, to deal with functions analytic and starlike with respect to symmetric conjugate points in the unit disc. Then, the same method is employed to functions meromorphic by Z.Z. Zou and Z.-R. Wu [Zhong Zhu Zou, Zhuo-Ren Wu, On meromorphically starlike functions and functions meromorphically starlike with respect to symmetric conjugate points, J. Math. Anal. Appl. 261 (2001) 17-27]. Now, the method can be employed to functions meromorphic harmonic in the punctured disc 0<|z|<1. Especially, a sharp coefficient estimate and a structural representation of such functions are obtained. 相似文献
7.
In this paper some new kinds of generalized Logarithmic and Harmonic Convex functions have been introduced and their relationships
with known concepts have been discussed. 相似文献
8.
Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Fréchet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X* and Y*) are isomorphic? We prove that if X* or Y* has the approximation property and Hwu(U) and Hwu(V) are topologically algebra isomorphic, then X* and Y* are isomorphic (the converse being true when U and V are the whole space). We get analogous results for Hb(U) and Hb(V), giving conditions under which an algebra isomorphism between Hb(X) and Hb(Y) is equivalent to an isomorphism between X* and Y*. We also obtain characterizations of different algebra homomorphisms as composition operators, study the structure of the spectrum of the algebras under consideration and show the existence of homomorphisms on Hb(X) with pathological behaviors. 相似文献
9.
Evgeny A. Poletsky 《Transactions of the American Mathematical Society》1997,349(11):4415-4427
For a compact set we construct a restoring covering for the space of real-valued functions on which can be uniformly approximated by harmonic functions. Functions from restricted to an element of this covering possess some analytic properties. In particular, every nonnegative function , equal to 0 on an open non-void set, is equal to 0 on . Moreover, when , the algebra of complex-valued functions on which can be uniformly approximated by holomorphic functions is analytic. These theorems allow us to prove that if a compact set has a nontrivial Jensen measure, then contains a nontrivial compact set with analytic algebra .
10.
There are basic equivalent assertions known for operator monotone functions and operator convex functions in two papers by Hansen and Pedersen. In this note we consider their results as correlation problem between two sequences of matrix n-monotone functions and matrix n-convex functions, and we focus the following three assertions at each label n among them:
- (i) f(0)0 and f is n-convex in [0,α),
- (ii) For each matrix a with its spectrum in [0,α) and a contraction c in the matrix algebra Mn,f(cac)cf(a)c,