On summability of a factored Fourier series
P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
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P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
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R. K. Jain, A. Ganguly (1978)
Matematički Vesnik
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B. Martić (1964)
Matematički Vesnik
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L. Jeśmanowicz (1962)
Annales Polonici Mathematici
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A. Nihal Tuncer (2002)
Annales Polonici Mathematici
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Using δ-quasi-monotone and any almost increasing sequences we prove a theorem on summability factors of infinite series, which generalizes a theorem of Mazhar [7] on summability factors.
Cihan Orhan (1998)
Czechoslovak Mathematical Journal
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In this paper, we give necessary and sufficient conditions on for , , to be translative. So we extend the known results of Al-Madi [1] and Cesco to the case .
Emre Taş (2018)
Mathematica Bohemica
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Our aim is to change classical test functions of Korovkin theorem on modular spaces by using -summability.
V. Swaminathan (1979)
Matematički Vesnik
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B. P. Mishra, D. Singh (1976)
Matematički Vesnik
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Masafumi Yoshino (2012)
Banach Center Publications
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This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)
Czechoslovak Mathematical Journal
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We prove and discuss some new -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...
Ferenc Móricz (2013)
Studia Mathematica
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Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function...
Ferenc Weisz (2009)
Studia Mathematica
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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space to . This implies the almost everywhere convergence of the Fejér means in a cone for all , which is larger than .
Włodzimierz Łenski, Bogdan Roszak (2008)
Banach Center Publications
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We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.