Relations among K and certain other methods for evaluations of sequences and series
B. Martić (1964)
Matematički Vesnik
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B. Martić (1964)
Matematički Vesnik
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R. K. Jain, A. Ganguly (1978)
Matematički Vesnik
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L. Jeśmanowicz (1962)
Annales Polonici Mathematici
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B. P. Mishra, D. Singh (1976)
Matematički Vesnik
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A. Sharma, Z. Ziegler (1987)
Studia Mathematica
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P. L. Sharma, R. K. Jain (1970)
Matematički Vesnik
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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 .
M. Malenica (1982)
Matematički Vesnik
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V. Swaminathan (1979)
Matematički Vesnik
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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...
Boumediene Abdellaoui, Ireneo Peral (2006)
Journal of the European Mathematical Society
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The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
C. T. Ng (1973)
Annales Polonici Mathematici
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Z. Kominek (1974)
Annales Polonici Mathematici
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H. Światak (1967)
Annales Polonici Mathematici
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Min Zhang, Jianguo Si (2014)
Annales Polonici Mathematici
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This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
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.
Yasutaka Sibuya (1984)
Recherche Coopérative sur Programme n°25
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Sergey V. Astashkin, Lech Maligranda (2014)
Banach Center Publications
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Geometric structure of Cesàro function spaces , where I = [0,1] and [0,∞), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q ∈ [1,∞] such that contains isomorphic and complemented copies of -spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces .