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In this paper we study convergence and summability problems of the series associated with the Laplace-Beltrami operator on the unique sphere. These series known as Fourier-Laplace series and we study the behaviour of these series in the different spaces of smooth functions with respect number of topologies. [ABSTRACT FROM AUTHOR]

In this article, we review the work on approximation of the Fourier-Laguerre series using various methods of summation like Cesàro, Nörlund's, Euler, Harmonic and product summability. In fact we establish the development of work on degree of approximation of Fourier-Laguerre series by different summability methods throughout time and how different methods, which were introduced, helped in better approximation of functions having Fourier-Laguerre series. This paper will help other researchers in selecting their research topic in this field. [ABSTRACT FROM AUTHOR]

This paper deals with the approximation of signal (or function) by generalized Nörlund Cesàro Euler product means of conjugate Fourier series. Under general conditions, some new theorems based on (N, pm, qm)(C, α, η)(E, θ) product summability have been established and demonstrated. The established theorem extends, generalizes and improves the existing result on summability of conjugate Fourier series. The findings may be a motivation for the researchers to work on the outcomes in the summability theory field. [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which defined by Çakallı [5] we introduce the concepts of pointwise w ρ α (f) -summability, pointwise ρ-statistical convergence of order α and uniform ρ-statistical convergence of order α sequences of real-valued functions. Also, we give some inclusion relations between these concepts. [ABSTRACT FROM AUTHOR]

The main object of this article is to introduce the concepts of (f, ρ)- statistical convergence of order α and strong (f, ρ)- summability of order α of sequences of real numbers and give some inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In [2], a main theorem dealing with |N¯, pn, θn|k summability factors of infinite series by using a quasi power increasing sequence has been proved. We have generalized this theorem to absolute matrix summability method by using under weaker conditions. We have also obtained some new results dealing with the different well known absolute summability methods. [ABSTRACT FROM AUTHOR]

In this study, we introduce and examine the concepts of Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability. Also some relations between Δm−weighted statistical convergence and Δm−weighted (N ¯ , p n) −summability are given. [ABSTRACT FROM AUTHOR]

In this study, by using definition of ρ-statistical convergence which was defined by Ç akallı[2], we give some inclusion relations between the set of ρ-statistical convergence and strong (S, [ρ]) summability. [ABSTRACT FROM AUTHOR]

We introduce the concept of regularly generated double integrals. We prove several Tauberian theorems for the (C, 1, 1) summability method for improper double integrals by using regularly generated integrals. [ABSTRACT FROM AUTHOR]

The space bv, the set of all bounded variation sequences, has an important role in the summability theory. In recent study, this spaces has been extended to the space bvθk and some matrix class on this space has been characterized [2]. In the present paper, for 1 ≤ k < ∞, computing Hausdorff measure of non-compactness, we characterize compact operators in the class (bv,bvθk), where θ is a sequence of positive numbers. [ABSTRACT FROM AUTHOR]

The space bv, the set of all bounded variation sequences, has an important role in the summability theory. In recent study, this spaces has been extended to the space bvθk and some matrix class on this space has been characterized [2]. In the present paper, for 1 ≤ k < ∞, computing Hausdorff measure of non-compactness, we characterize compact operators in the class (bv,bvθk), where θ is a sequence of positive numbers. [ABSTRACT FROM AUTHOR]

Extending the result of Bor [1] (2016), a result concerning absolute indexed Riesz Summability factors... using quasi - f - power increasing sequence, has been established. [ABSTRACT FROM AUTHOR]

In the present paper, we have generalized two main theorems dealing with weighted mean summability for absolute matrix summability which play a vital role in the field of theory and application of summability by using quasi-monotone sequences. These sequences have assumed great importance because of their applicability and usefulness in other fields. [ABSTRACT FROM AUTHOR]

In the present paper, we prove a general theorem dealing with absolute matrix summability methods of infinite series by using the concept of quasi power increasing sequence instead of almost increasing sequence. Some important known theorems are deduced from our theorem. [ABSTRACT FROM AUTHOR]

In [1], Bor has proved a theorem concerning absolute summability of infinite series. In the present paper, this known theorem has been generalized to absolute matrix summability by using matrix transformations and almost increasing sequences. Some results have also been obtained. [ABSTRACT FROM AUTHOR]

In this study we introduce the concepts of Wijsman asymptotically deferred statistical equivalence of order α and Wijsman strong deferred Cesàro asymptotically equivalence of order α for set sequences. [ABSTRACT FROM AUTHOR]

In the present paper, we extend the notions of statistically convergence of order β and strong Cesàro summability of order β for sequences of fuzzy numbers and introduce the notions of f-statistically convergence of order β and strong Cesàro summability of order β for β ∈ (0,1] with respect to an unbounded modulus function f for double sequences of fuzzy numbers and give some inclusion theorems. [ABSTRACT FROM AUTHOR]

The purpose of this work is to introduce the concepts of …-lacunary statistical convergence of order α and lacunary strongly (…)-convergence of order α. We establish some connections between lacunary strongly (…) - convergence of order α and (…)-lacunary statistical convergence of order α. It is shown that if a sequence is lacunary strongly (…)-summable of order α then it is (…)-lacunary statistically convergent of order α. [ABSTRACT FROM AUTHOR]

In this study, using the generalized difference operator Δmi and a sequence λ = (λn) which is a non-decreasing sequence of positive numbers tending to 8 such that λn+1 = λn + 1, λ1 = 1, we introduce the concepts of λ(Δmi) -statistical convergence of order α (α Є (0,1]) and strong λ (Δmi) -Cesaro summablility of order α (α > 0). We establish some connections between λ (Δim) -statistical convergence of order a and strong λ (Δmi) - Cesaro summablility of order a. It is shown that if a sequence is strongly λ (Δmi) -Cesaro summable of order a, then it is λ (Δim) - statistically convergent of order i in case 0 < α ≤ β ≤ 1. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the concepts of f-lacunary statistical convergence of order (α, β) and strong f--lacunary summability of order (α, β) of sequences of real numbers for 0 < a ≤ β ≤ 1, where f is an unbounded modulus. [ABSTRACT FROM AUTHOR]

Móricz [3] characterized summability (C, 1) of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L, 1) of integrals. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the Hardy-Littlewood-Polya inequality and Nursultanov inequality is proved. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [M. Balcerzak, P. Das, M. Filipczak, and J. Swaczyna, Acta Math. Hungar. 147, 97-115 (2015)], we further generalize the recently introduced summability method of [E. Savas, and P. Das, Appl. Math. Lett. 24, 826-830 (2011)] and introduce the new notion namely, Iλ-statistical convergence of weight g, where g : N→[0;∞) is a function satisfying g(n)→∞ and g(n)90 as n→∞. We mainly investigate certain properties of this convergence. [ABSTRACT FROM AUTHOR]

Let 0 < p ≤ 1. In the present paper, we introduce the space ℓp as the domain of the triangle eB which is the composition of E1, C1 and Δ of the Euler, Cesàro means of order one and the backward difference matrix. Furthermore, we give an inclusion relation concerning the space ℓp and compute the alpha-, beta- and gamma-duals of the space ℓp and construct its basis. We characterize the classes (ℓp : l&#8734), (ℓp : c) and (ℓp : c0) of infinite matrices, and give the characterization of some other classes of matrix transformations from the space ℓp to the Euler, Riesz, difference, etc., sequence spaces, by means of a basic lemma. [ABSTRACT FROM AUTHOR]

Trigonometric Fourier approximation and Lipchitz class of function had been introduced by Zygmund and McFadden respectively. Dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. have established certain theorems. Extending their results, in this paper a theorem on trigonometric approximation of conjugate series of Fourier series of a function f ∊W (LP, ξ(t) by product summability (E,s)(N, pn, qn) has been established. [ABSTRACT FROM AUTHOR]

In this work necessary and sufficient conditions of absolute summability of multiple trigonometric Fourier series of functions from anisotropic spaces of Lebesque are found in terms of its best approximation, the module of smoothness and the mixed smoothness module. [ABSTRACT FROM AUTHOR]

We give some conditions under which Abel summable sequences of fuzzy numbers are convergent. As corollaries we obtain the results given in [E. Yavuz, Ö. Talo, Abel summability of sequences of fuzzy numbers, Soft computing 2014, doi: 10.1007/s00500-014-1563-7]. [ABSTRACT FROM AUTHOR]

A real valued function f defined on a subset of R, the set of real numbers is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (ak) of point in R is called Abel statistically quasi-Cauchy if Abel density of the set {k ∞ N : ∣△αk∣ ≥ ε} is 0 for every ε > 0. In this paper, we give an investigation of Abel statistical ward continuity. Some other types of continuities are also studied and interesting results are obtained. It turns out that the set of Abel statistical ward continuous functions is a closed subset of the set of continuous functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function ƒ on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences of points in A. We also studied some other kinds of continuities. [ABSTRACT FROM AUTHOR]

In this paper, we shall make a new approach to two well known summability methods by using ideals and introduce new notions, namely, I-statistical convergence and I-lacunary statistical convergence by taking a nonnegative real-valued Lebesque measurable function in the interval (1, ∞) and mainly investigate their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

In the present paper, we summarize the literature concerning two dimensional dual matrices and related results. Finally, after giving the general statement of usual dual summability methods we emphasize on four dimensional dual matrices, as a new development of the concept of dual matrices. [ABSTRACT FROM AUTHOR]

As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G). [ABSTRACT FROM AUTHOR]

Following Section 4.8 of Başsar [Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, İstanbul-2012, ISBN: 978-1-60805-252-3], we define the duality relation of the new kind between a pair of infinite matrices. Our focus is the dual summability methods derived by the Euler means of order r. By means of a strongly regular triangle matrix C = (cnk), we obtain the composited matrices. The main purpose of this study is to give some inclusion theorems concerning the composited and original dual summability methods defined by the Euler means of order r. [ABSTRACT FROM AUTHOR]

Several improvements are achieved concerning the result of Bor and Leindler [3]. [ABSTRACT FROM AUTHOR]

In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable real-valued integrals over R+ := [0, ∞). Some particular choices of weight functions provide alternative proofs of some well-known Tauberian theorems given for several important summability methods. [ABSTRACT FROM AUTHOR]

In a recent paper [A reducibility of the Kampé de Fériet function, Advances in Comput. Math. and its Applications, Vol. 1, No. 1, pp. 76-79 (2012)], the author has evaluated one very interesting reduction formula. In this paper, two new reduction formulas of Kampe de Feriet function have been evaluated by using Gauss's second summation theorem on the sum of a 3F2. The results established in this paper are simple, interesting, easily established and may be useful. [ABSTRACT FROM AUTHOR]

We predict the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large-Hadron-Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. [ABSTRACT FROM AUTHOR]

By (U, V) we denote the set of all sequences ε = (εn) such that ∑εnan is summable V whenever ∑an is summable U, where U and V are two summability methods. In this study, we get necessary and sufficient conditions for ε ∈ (|N, qn, θn|k, |N̄, pn|) and ε ∈ (|N̄, pn|, |N, qn, θn|k), where |N̄, pn| and |N, qn, θn|k are absolute weighted and Nörlund summability methods, respectively. Thus, in the special case, some well known results are also deduced. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to obtain family of summation formulas with unit argument for 2F1 by well known formulas by using Kummer's second summation theorem, 2F1[a,b;1+a-b;-1]. [ABSTRACT FROM AUTHOR]