Abstract
We introduce the concept of weak monotone sequences with respect to a given nondecreasing sequence {mn} as well as similar concept for functions. For such sequences/functions we prove several convergence tests for number series such as Cauchy, Maclaurin, Schlömilch, the Abel–Oliver nth term test. We also study Hardy’s inequalities for weak monotone sequences/ functions.
Mathematics Subject Classification (2010). Primary 40A05, 26A48; Secondary 26D15.
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© 2014 Springer International Publishing Switzerland
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Tikhonov, S., Zeltser, M. (2014). Weak Monotonicity Concept and Its Applications. In: Ruzhansky, M., Turunen, V. (eds) Fourier Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02550-6_18
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DOI: https://doi.org/10.1007/978-3-319-02550-6_18
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-02549-0
Online ISBN: 978-3-319-02550-6
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