Weak Monotonicity Concept and Its Applications

  • S. TikhonovEmail author
  • M. Zeltser
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Weak monotone sequences/functions equiconvergence of sums and integrals Hardy’s inequality 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.ICREA and Centre de Recerca Matemática (CRM)Bellaterra (Barcelona)Spain
  2. 2.Department of MathematicsTallinn UniversityTallinnEstonia

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