Weak sequential convergence in the dual of a Banach space does not imply norm convergence
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چکیده
منابع مشابه
Convergence of the Costates Does Not Imply Convergence of the Control
S OLVING an optimal control problem using a digital computer implies discrete approximations. Since the 1960s, there have been well-documented [1–3] naïve applications of Pontryagin’s principle in the discrete domain. Although its incorrect applications continue to this day, the origin of the naïvete is quite understandable because one has a reasonable expectation of the validity of Pontryagin’...
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A net (xα) in a vector lattice X is unbounded order convergent to x ∈ X if |xα − x| ∧ u converges to 0 in order for all u ∈ X+. This convergence has been investigated and applied in several recent papers by Gao et al. It may be viewed as a generalization of almost everywhere convergence to general vector lattices. In this paper, we study a variation of this convergence for Banach lattices. A ne...
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Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.
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چکیده ندارد.
Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space
We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13691-3