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Universally divergent Fourier series via Landau's extremal functions

Gerd Herzog, Peer Chr. Kunstmann (2015)

Commentationes Mathematicae Universitatis Carolinae

We prove the existence of functions f A ( 𝔻 ) , the Fourier series of which being universally divergent on countable subsets of 𝕋 = 𝔻 . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on 𝕋 { 1 } .

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

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