Lacunary statistical convergence and strongly lacunary summable functions of order α
Filomat, 2017 Summary: The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order \(\alpha\) and lacunary statistical convergence of order \(\alpha\) of real-valued functions which are measurable (in the Lebesgue sense) in the interval \((1, \infty)\). Some relations between lacunary statistical convergence of
H. M. Srivastava, Mikâil Et
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A triple lacunary generating function for Hermite polynomials [PDF]
The Electronic Journal of Combinatorics, 2004 Some of the classical orthogonal polynomials such as Hermite, Laguerre, Charlier, etc. have been shown to be the generating polynomials for certain combinatorial objects. These combinatorial interpretations are used to prove new identities and generating functions involving these polynomials.
Ira M. Gessel, Pallavi Jayawant
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New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences [PDF]
Axioms, 2018 In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical ...
Ömer Kişi +2 more
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Lacunary Generating Functions for the Laguerre Polynomials [PDF]
, 2013 Symbolic methods of umbral nature play an important and increasing role in the theory of special functions and in related fields like combinatorics. We discuss an application of these methods to the theory of lacunary generating functions for the Laguerre polynomials for which we give a number of new closed form expressions.
D. Babusci +3 more
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I-lacunary summability function of order α
Filomat, 2017 In this paper, we further generalize recently introduced summability methods in [23](where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of order ?, where 0 < ? < 1 by taking nonnegative real-valued Lebesque measurable function in the interval (1,?).
Ekrem Savaş
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Lacunary Statistical Convergence of Sequences of Real-Valued Functions [PDF]
Journal of Mathematics, 2013 We introduce the concepts of the lacunary statistical convergence of sequences of real-valued functions. We also give the relation between this convergence and strongly lacunary and pointwise statistical convergence. Furthermore we introduce the concept of a lacunary statistical Cauchy sequence for functional sequences and prove that it is equivalent ...
A. Gökhan
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Centered Polygonal Lacunary Graphs: A Graph Theoretic Approach to p-Sequences of Centered Polygonal Lacunary Functions [PDF]
Mathematics, 2019 This work is on the nature and properties of graphs which arise in the study of centered polygonal lacunary functions. Such graphs carry both graph-theoretic properties and properties related to the so-called p-sequences found in the study of centered ...
Keith Sullivan +2 more
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Bounds for Lacunary maximal functions given by Birch–Magyar averages [PDF]
Transactions of the American Mathematical Society, 2020 We obtain positive and negative results concerning lacunary discrete maximal operators defined by dilations of sufficiently nonsingular hypersurfaces arising from Diophantine equations in many variables. Our negative results show that this problem differs substantially from that of lacunary discrete maximal operators defined along a nonsingular ...
Brian Cook, Kevin Hughes
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lacunary directional maximal function on the Heisenberg group [PDF]
Mathematical Research Letters, 2004 Let \(K=(k_1,k_2,k_3)\in{\mathbb Z}^3\) and \(v_K=(2^{k_1}, 2^{k_2}, 2^{k_3}).\) Let \(\mathbb H^1\) be the Heisenberg group identified with \({\mathbb R}^2\times {\mathbb R}^1\) endowed with the group multiplication: \[ (p,q,t)\cdot(p',q',t')=(p+p',q+q', t+t'+2(p'\cdot q-p\cdot q')).
Joonil Kim
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On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δnm-statistical convergence [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In this article, we introduce the lacunary difference sequence spaces w0(M, θ, Δnm, p, q), w1(M, θ, Δnm, p, q) and w∞(M, θ, Δnm, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define
Tripathy Binod Chandra, Dutta Hemen
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