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a) For all increasing (resp. By virtue of Lemma 4.7, Proposition 5.3 and Lemma 5.4, it is clear that the mapping ˜ J is a linear injection and a Banach lattice homomorphism. That
For sequences defined in terms of 2-adic valuations, we exploit the intrinsic periodic behaviour obtained by a double summation.. The tool is the
In this section, we will prove Theorem 1, but first we note the following lemma, which is a direct consequence of the definitions of the Stern sequence and its twist..
For the convenience of the reader we quote some known results as the following lemmas:..
Lomadze, Summation of singular series corresponding to represen- tations of numbers by some quadratic forms in twelve variables.. Lomadze, On the number of representations of
The paper extends certain stochastic convergence (here, statistical convergence) of sequences of R k -valued ran- dom variables namely, the convergence in probability, in L p and
This paper assists land-grant university National Cooperative Research Extension Education Service (NCREES) faculty in understanding the definition of a consumer society, the
The publisher regrets that in the above article an error was made on page 77, column 2, in the equation under the following sentence:. “By
