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961.
A. A. Egorov 《Siberian Mathematical Journal》2008,49(4):637-649
We obtain stability theorems for classes of solutions to the differential equations constructed by means of quasiconvex functions and null Lagrangians. 相似文献
962.
Bounded and compact Carleson measures in the unit ball B of R n , n ≥ 2, are characterized by means of global Dirichlet integrals of the conformal self‐map Ta taking a ∈ B to the origin. The same proof applies in the unit ball of C n . It is also proved that the powers of the Jacobian of Ta satisfy the weak Harnack inequality and even Harnack's inequality with a constant independent of a. As an application of these results it is shown that the two different definitions for Carleson measures in the existing literature are equivalent for a certain range of parameter values. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
963.
This paper studies the stability of the set containment problem. Given two non-empty sets in the Euclidean space which are
the solution sets of two systems of (possibly infinite) inequalities, the Farkas type results allow to decide whether one
of the two sets is contained or not in the other one (which constitutes the so-called containment problem). In those situations
where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining
whether the relative position of the two sets is preserved by sufficiently small perturbations or not. This paper deals with
this stability problem as a particular case of the maintaining of the relative position of the images of two set-valued mappings;
first for general set-valued mappings and second for solution sets mappings of convex and linear systems. Thus the results
in this paper could be useful in the postoptimal analysis of optimization problems with inclusion constraints.
相似文献
964.
具随机性误差隐迭代程序的收敛性 总被引:2,自引:0,他引:2
在任意Banauch空间中,证明了有限族渐近半压缩映象具随机性误差的隐迭代程序逼近其公共不动点的强收敛性定理.所得结论推广和改进了引文中的相应结果. 相似文献
965.
In this paper, we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a Hilbert space. Moreover, we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings. Our results extend and improve the recent ones announced by Kim and Xu [T.W. Kim, H.W. Xu, Strong convergence of modified Mann iteration for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140–1152], Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379], and many others. 相似文献
966.
We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them.
Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper.
相似文献
967.
In this paper a common generalization of the algebraic and topological pseudomonotonicity for set-valued maps is introduced. Existence results for variational inequalities governed by such maps are given. 相似文献
968.
Qing-Hua Xu 《Journal of Mathematical Analysis and Applications》2007,334(2):1096-1105
In this paper, we give characterization of almost starlike functions of order α (respectively almost starlike mappings of order α) on the unit disc in C (respectively the unit ball in a finite-dimensional complex Banach space) in terms of Löwner chains. Furthermore, using the properties of Löwner chains, we can easily prove that two classes of generalized Roper-Suffridge extension operators preserve almost starlikeness of order α on two important classes of Reinhardt domains in Cn, respectively. 相似文献
969.
Zhenyu Huang 《Journal of Mathematical Analysis and Applications》2007,329(2):935-947
In this paper, the equivalence of the strong convergence between the modified Mann and Ishikawa iterations with errors in two different schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91-101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125] respectively is proven for the generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumption. Our results generalize the recent results of the papers [Zhenyu Huang, F. Bu, The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl. 325 (1) (2007) 586-594; B.E. Rhoades, S.M. Soltuz, The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl. 289 (2004) 266-278; B.E. Rhoades, S.M. Soltuz, The equivalence between Mann-Ishikawa iterations and multi-step iteration, Nonlinear Anal. 58 (2004) 219-228] by extending to the most general class of the generalized strongly successively Φ-pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u1, x1 in uniformly smooth Banach spaces. 相似文献
970.
Bilâl Altay 《Journal of Mathematical Analysis and Applications》2007,336(1):632-645
The matrix domain of the particular limitation methods Cesàro, Riesz, difference, summation and Euler were studied by several authors. In the present paper, certain topological properties and β- and γ-duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes. 相似文献