Now showing items 1-4 of 4
A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-02-18)
The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation z 4 −2L z 3 +( L 2 − a 2 − b 2 ) z 2 +2L a 2 z− L 2 a 2 =0 z4−2Lz3+(L2−a2−b2)z2+2La2z−L2a2=0 are developed. For the case L≥ L min L≥Lmin , these methods imply a complete parametric representation for integer ...
Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-20)
In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces L q,r (logL ) α Lq,r(logL)α involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for ...
Some inequalities related to strong convergence of Riesz logarithmic means
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-23)
In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series.
SOME NEW REFINEMENTS OF HARDY-TYPE INEQUALITIES
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-02-11)
We obtain some further reﬁnements of Hardy-type inequalities via superqudraticity technique. Our results both unify and further generalize several results on reﬁnements of Hardy-type inequalities in the literature.