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Displaying similar documents to “Strongly convergent generalized difference sequence spaces defined by a modulus.”

Asymptotic properties of solutions of nonautonomous difference equations

Janusz Migda (2010)

Archivum Mathematicum

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Asymptotic properties of solutions of difference equation of the form Δ m x n = a n ϕ n ( x σ ( n ) ) + b n are studied. Conditions under which every (every bounded) solution of the equation Δ m y n = b n is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than m is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically...

The Sum and Product of Finite Sequences of Complex Numbers

Keiichi Miyajima, Takahiro Kato (2010)

Formalized Mathematics

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This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].