Results 11 to 20 of about 108,393 (45)
The τ‐fixed point property for nonexpansive mappings
Abstract and Applied Analysis, Volume 3, Issue 3-4, Page 343-362, 1998., 1998 Let X be a Banach space and τ a topology on X. We say that X has the τ‐fixed point property (τ‐FPP) if every nonexpansive mapping T defined from a bounded convex τ‐sequentially compact subset C of X into C has a fixed point. When τ satisfies certain regularity conditions, we show that normal structure assures the τ‐FPP and Goebel‐Karlovitz′s Lemma ...
Tomás Domínguez Benavides +2 more
wiley +1 more source
Non‐archimedean Eberlein‐ mulian theory
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 637-642, 1996., 1995 It is shown that, for a large class of non‐archimedean normed spaces E, a subset X is weakly compact as soon as f(X) is compact for all f ∈ E′ (Theorem 2.1), a fact that has no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive a non‐archimedean version of the Eberlein‐ mulian Theorem (2.2 and 2.3, for the ...
T. Kiyosawa, W. H. Schikhof
wiley +1 more source
Pareto optimality for nonlinear infinite dimensional control systems
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 233-242, 1990., 1989 In this note we establish the existence of Pareto optimal solutions for nonlinear, infinite dimensional control systems with state dependent control constraints and an integral criterion taking values in a separable, reflexive Banach lattice. An example is also presented in detail. Our result extends earlier ones obtained by Cesari and Suryanarayana.
Evgenios P. Avgerinos +1 more
wiley +1 more source
Measurable multifunctions and their applications to convex integral functionals
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 1, Page 175-191, 1989., 1988 The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue‐Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some ...
Nikolaos S. Papageorgiou
wiley +1 more source
Convergence theorems for Banach space valued integrable multifunctions
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 3, Page 433-442, 1987., 1987 In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue‐Bochner spaces . Then we use that result to prove Fatou′s type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions.
Nikolaos S. Papageorgiou
wiley +1 more source
The last proof of extreme value theorem and intermediate value theorem [PDF]
arXiv, 2022 The paper gives a unified and simple proof of both theorems and Cousin's theorem.
arxiv
arXiv, 2022 Many theorems in complex analysis propagate analyticity, such as the Forelli theorem, edge-of-the-wedge theorem and so on. We give a germination theorem which allows for general analytic propagation in complete normed fields. In turn, we develop general analogs of the Forelli theorem, edge-of-the-wedge theorem, and the royal road theorem, and gain ...
arxiv
An analogue of Mahler's transference theorem for multiplicative Diophantine approximation [PDF]
arXiv, 2023 Khintchine's and Dyson's transference theorems can be very easily deduced from Mahler's transference theorem. In the multiplicative setting an obstacle appears, which does not allow deducing the multiplicative transference theorem immediately from Mahler's theorem. Some extra considerations are required, for instance, induction by the dimension.
arxiv
Index theorem for inhomogeneous hypoelliptic differential operators [PDF]
arXiv, 2020 We prove an index theorem for inhomogeneous differential operators satisfying the Rockland condition (hence hypoelliptic). This theorem extends an index theorem for contact manifolds by Van-Erp.
arxiv
Supermodular Extension of Vizing's Edge-Coloring Theorem [PDF]
arXiv, 2022 K\H{o}nig's edge-coloring theorem for bipartite graphs and Vizing's edge-coloring theorem for general graphs are celebrated results in graph theory and combinatorial optimization. Schrijver generalized K\H{o}nig's theorem to a framework defined with a pair of intersecting supermodular functions. The result is called the supermodular coloring theorem.
arxiv