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1.
Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption 总被引:4,自引:0,他引:4
In the present paper, the following result is shown: Let be a real Banach space with a uniformly convex dual , and let be a nonempty closed convex and bounded subset of . Assume that is a continuous strong pseudocontraction. Let and be two real sequences satisfying (i) for all ; (ii) ; and (iii) as Then the Ishikawa iterative sequence generated by
converges strongly to the unique fixed point of .
2.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》1997,125(5):1355-1361
Let and fix an interval . If is the operator on defined by , then maps into .
3.
Pham Anh Minh 《Proceedings of the American Mathematical Society》1997,125(6):1577-1578
Let be a homomorphism of -groups such that
is injective, for . We prove that the non-bijectivity of implies the existence of a quotient of containing as a proper direct factor. This gives a refined proof of a result of Evens, which asserts that is bijective if is.
is injective, for . We prove that the non-bijectivity of implies the existence of a quotient of containing as a proper direct factor. This gives a refined proof of a result of Evens, which asserts that is bijective if is.
4.
Michael E. Taylor 《Proceedings of the American Mathematical Society》1997,125(6):1711-1716
We show that, if is the representation of on given by (2.11), and is a bounded operator on , then belongs to if and only if
is a function on with values in the Banach space .
5.
Changyu Xia 《Proceedings of the American Mathematical Society》1997,125(6):1801-1806
Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.
6.
Gabriel Navarro Wolfgang Willems 《Proceedings of the American Mathematical Society》1997,125(6):1589-1591
Let and be distinct prime numbers and let be a finite group. If is a -block of and is a -block, we study when the set of ordinary irreducible characters in the blocks and coincide.
7.
Nazih Nahlus 《Proceedings of the American Mathematical Society》1997,125(9):2767-2769
Let be any analytic group, let be a maximal toroid of the radical of , and let be a maximal semisimple analytic subgroup of . If is the Lie algebra of , is the radical of , and is the center of , we show that has a faithful representation if and only if (i) , and (ii) has a faithful representation.
8.
Jü rgen Herzog Takayuki Hibi 《Proceedings of the American Mathematical Society》1997,125(6):1579-1583
Here we study the maximal dimension of the annihilator ideals
of artinian graded rings with a given Hilbert function, where is the polynomial ring in the variables over a field with each , is a graded ideal of , and is the graded maximal ideal of . As an application to combinatorics, we introduce the notion of -facets and obtain some informations on the number of -facets of simplicial complexes with a given -vector.
of artinian graded rings with a given Hilbert function, where is the polynomial ring in the variables over a field with each , is a graded ideal of , and is the graded maximal ideal of . As an application to combinatorics, we introduce the notion of -facets and obtain some informations on the number of -facets of simplicial complexes with a given -vector.
9.
James E. Joseph Myung H. Kwack 《Proceedings of the American Mathematical Society》1997,125(6):1675-1684
Let represent the family of holomorphic (continuous) maps from a complex (topological) space to a complex (topological) space , and let be the Alexandroff one-point compactification of if is not compact, if is compact. We say that is uniformly normal if , is relatively compact in (with the compact-open topology) for each complex manifold . We show that normal maps as defined and studied by authors in various settings are, as singleton sets, uniformly normal families, and prove extension and convergence theorems for uniformly normal families. These theorems include (1) extension theorems of big Picard type for such families - defined on complex manifolds having divisors with normal crossings - which encompass results of Järvi, Kiernan, Kobayashi, and Kwack as special cases, and (2) generalizations to such families of an extension-convergence theorem due to Noguchi.
10.
Gert K. Pedersen 《Proceedings of the American Mathematical Society》1997,125(9):2657-2660
Given a pair , of -commuting, hereditary -subalgebras of a unital -algebra , such that is -unital and , there is an element in , with , such that is strictly positive in and is strictly positive in in . Moreover, is strictly positive in in .
11.
M. Cabrera J. Martí nez 《Proceedings of the American Mathematical Society》1997,125(7):2033-2039
We show that, for every ultraprime Banach algebra , there exists a positive number satisfying for all in , where denotes the centre of and denotes the inner derivation on induced by . Moreover, the number depends only on the ``constant of ultraprimeness' of .
12.
Peter Danchev 《Proceedings of the American Mathematical Society》1997,125(9):2559-2564
In this note we study the commutative modular and semisimple group rings of -summable abelian -groups, which group class was introduced by R. Linton and Ch. Megibben. It is proved that is -summable if and only if is -summable, provided is an abelian group and is a commutative ring with 1 of prime characteristic , having a trivial nilradical. If is a -summable -group and the group algebras and over a field of characteristic are -isomorphic, then is a -summable -group, too. In particular provided is totally projective of a countable length.
Moreover, when is a first kind field with respect to and is -torsion, is -summable if and only if is a direct sum of cyclic groups.
13.
Tadasi Huruya 《Proceedings of the American Mathematical Society》1997,125(12):3617-3624
Let be a -hyponormal operator on a Hilbert space with polar decomposition and let for and We study order and spectral properties of In particular we refine recent Furuta's result on -hyponormal operators.
14.
M. Boratynski 《Proceedings of the American Mathematical Society》1997,125(2):329-338
Suppose a smooth curve is a set-theoretic complete intersection of two surfaces and with the multiplicity of along less than or equal to the multiplicity of along . One obtains a relation between the degrees of , and , the genus of , and the multiplicity of along in case has only ordinary singularities. One obtains (in the characteristic zero case) that a nonsingular rational curve of degree 4 in is not set-theoretically an intersection of 2 surfaces, provided one of them has at most ordinary singularities. The same result holds for a general nonsingular rational curve of degree .
15.
J. Haefner A. del Rí o J. J. Simó n 《Proceedings of the American Mathematical Society》1997,125(6):1651-1658
This paper investigates the ring-theoretic similarities and the categorical dissimilarities between the ring of row finite matrices and the ring of row and column finite matrices. For example, we prove that two rings and are Morita equivalent if and only if the rings and are isomorphic. This resembles the result of V. P. Camillo (1984) for . We also show that the Picard groups of and are isomorphic, even though the rings and are never Morita equivalent.
16.
Hans-Peter A. Kü nzi Leonid B. Shapiro 《Proceedings of the American Mathematical Society》1997,125(6):1853-1859
For a metric space let (that is, the set of all graphs of real-valued continuous functions with a compact domain in ) be equipped with the Hausdorff metric induced by the hyperspace of nonempty closed subsets of It is shown that there exists a continuous mapping satisfying the following conditions: (i) for all partial functions (ii) For every nonempty compact subset of is a linear positive operator such that .
17.
G. Mikhalkin 《Proceedings of the American Mathematical Society》1997,125(6):1831-1833
The adjunction formula computes the genus of an almost complex curve embedded in an almost complex surface in terms of the homology class of . If is Kähler (or at least symplectic) and the self-intersection of is non-negative then the genus of any other surface embedded in and homologous to is not less then the genus of (the proof of this statement (which is a generalization of the Thom conjecture for ) was recently given by the Seiberg-Witten theory). This paper shows that the extra assumptions on are essential for the genus-minimizing properties of embedded almost complex curves.
18.
Athanassios G. Kartsatos 《Proceedings of the American Mathematical Society》1997,125(5):1469-1478
Let be a real, reflexive, locally uniformly convex Banach space with locally uniformly convex. Let be a maximal monotone operator and open and bounded. Assume that is pathwise connected and such that and Then If, moreover, is of type () on then may be replaced above by The significance of this result lies in the fact that it holds for multi-valued mappings which do not have to satisfy It has also been used in this paper in order to establish a general ``invariance of domain' result for maximal monotone operators, and may be applied to a greater variety of problems involving partial differential equations. No degree theory has been used. In addition to the above, necessary and sufficient conditions are given for the existence of a zero (in an open and bounded set ) of a completely continuous perturbation of a maximal monotone operator such that is locally monotone on
19.
M. Babikov 《Proceedings of the American Mathematical Society》1997,125(6):1571-1575
In this paper we show how to construct an isomorphism between an alternative algebra over a field of characteristic and its isotope , where is an element of Zhevlakov's radical of . This leads to the equivalence of any polynomial identity in alternative algebras and the isotope identity .
20.
D. D. Anderson Moshe Roitman 《Proceedings of the American Mathematical Society》1997,125(10):2853-2854
An ideal of a commutative ring with identity is called a cancellation ideal if whenever for ideals and of , then . We show that an ideal is a cancellation ideal if and only if is locally a regular principal ideal.