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In this paper, the problem of -convergence of Fourier series with quasi-monotone coefficients is handled by using the -mean. Also, an example is given about the Fourier series of a signal (function) and its mean. [ABSTRACT FROM AUTHOR]

We focus on the Tauberian work for which Jaap Korevaar is best known, together with its connections with probability theory. We begin with a brief sketch of the field up to Beurling's work. We follow with three sections on Beurling aspects: Beurling slow variation; the Beurling Tauberian theorem for which it was developed; Riesz means and Beurling moving averages. We then give three applications from probability theory: extremes, laws of large numbers, and large deviations. We then turn briefly to other areas of Korevaar's work. We close with a personal postscript (whence our title). [ABSTRACT FROM AUTHOR]

In this paper, a general theorem dealing with γ - / A, pn/k summability of an infinite series has been proved by using an almost increasing sequence. Also, some results have been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we intend to make new approach to introduce and study some fractional difference sequence spaces by Riesz mean associated with inĄnite matrix and a sequence of modulus functions over n -normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored and some inclusion relations concerning these spaces are also establish. Finally, we make an effort to study the statistical convergence through fractional difference operator. [ABSTRACT FROM AUTHOR]

Let $ f(z) $ be a holomorphic Hecke eigenform of weight $ k $ with respect to the full modular group $ SL(2, Z) $, and let $ \Delta_{\rho}(x; sym^{2}f) $ be the error term of the Riesz mean of the symmetric square $ L $-function $ L(s, sym^{2}f) $. In this paper, using a Voronoï type formula for $ \Delta_{\rho}(x; sym^{2}f) $, we consider the third-power moment of $ \Delta_{\rho}(x; sym^{2}f) $ and derive the asymptotic formula for $ \int_{1}^{T}\Delta_{\rho}^{3}(x;sym^{2}f)dx. $

In the present article, (ϕ, δ)-monotone sequences are studied. A theorem on absolute Riesz summability of an infinite series is proven under some suitable conditions by using a (ϕ, δ)-monotone sequence. [ABSTRACT FROM AUTHOR]

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi $\beta$-power increasing sequences. Also, a known result dealing with absolute Riesz summability has been given.

In the present paper, two theorems of absolute summability have been proved by using the definition of almost increasing sequence.

In the present paper, we have proved a basic theorem on the absolute Riesz summability factors of infinite series by using a wider class of power increasing sequences and then we applied this new result to the trigonometric Fourier series. Some new results are also obtained concerning the factored infinite series and trigonometric Fourier series. [ABSTRACT FROM AUTHOR]

We show that, in every weighted Dirichlet space on the unit disk with superharmonic weight, the Taylor series of a function in the space is (C , α) -summable to the function in the norm of the space, provided that α > 1 / 2 . We further show that the constant 1/2 is sharp, in marked contrast with the classical case of the disk algebra. [ABSTRACT FROM AUTHOR]

In [1], Mazhar has proved two theorems on absolute summability of infinite series. In the present paper, these two theorems have been generalized for absolute matrix summability of the series by using almost increasing sequence. [ABSTRACT FROM AUTHOR]

In this paper we prove a general new summability factor theorem for infinite series involving quasi-power increasing sequences. Some new results are also deduced. [ABSTRACT FROM AUTHOR]

We study bounds on the Riesz means of the mixed Steklov–Neumann and Steklov–Dirichlet eigenvalue problem on a bounded domain Ω in ℝ n . The Steklov–Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov–Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov–Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian, and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the Appendix which in particular show the asymptotic sharpness of the bounds we obtain. [ABSTRACT FROM AUTHOR]

In this study, we propose a new method, i.e. Adaptive Riesz Mean Filter (ARmF), by operationalizing pixel similarity for salt-and-pepper noise (SPN) removal. Afterwards, we compare the results of ARmF, A New Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Based on Pixel Density Filter (BPDF), Modified Decision-Based Unsymmetric Trimmed Median Filter (MDBUTMF) and Decision-Based Algorithm (DBA) by using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), Image Enhancement Factor (IEF), and Visual Information Fidelity (VIF) for 20 traditional test images (Lena, Cameraman, Barbara, Baboon, Peppers, Living Room, Lake, Plane, Hill, Pirate, Boat, House, Bridge, Elaine, Flintstones, Flower, Parrot, Dark-Haired Woman, Blonde Woman, and Einstein), 40 test images in the TESTIMAGES Database, and 200 RGB test images from the UC Berkeley Dataset ranging in noise density from 10% to 90%. Moreover, we compare the running time of these algorithms. These results show that ARmF outperforms the methods mentioned above. We finally discuss the need for further research. [ABSTRACT FROM AUTHOR]

In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the |N ¯ , pn; θn|k summability method. Some new and known results are also obtained. [ABSTRACT FROM AUTHOR]

We investigate the approximation properties of Nörlund and Riesz means of trigonometric Fourier series are investigated in the subset of weighted Lebesgue space with variable exponent. [ABSTRACT FROM AUTHOR]

In this paper, a known theorem dealing with weighted mean summability methods of non-decreasing sequences has been generalized for |A, pn; δ|k summability factors of almost increasing sequences. Also, some new results have been obtained concerning |N̅, pn|k, |N̅, pn; δ|k and |C,1; δ|k summability factors. [ABSTRACT FROM AUTHOR]

We prove a general theorem dealing with an application of quasi β-power increasing sequences. This theorem also includes several new and known results. [ABSTRACT FROM AUTHOR]

In this paper we establish some wide-ranging spaces of sequences generated by Riesz mean associated with lacunary sequences and multiplier sequences of Orlicz function. We have encompassed some topological and algebraic properties of these sequence spaces. We also make an effort to prove that these spaces are Banach and AK-BK spaces. Finally, we prove that these sequence spaces are topologically isomorphic. [ABSTRACT FROM AUTHOR]

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi b-power increasing sequences. Also, a known result dealingwith absolute Riesz summability has been given. [ABSTRACT FROM AUTHOR]

In this paper, we prove a generel theorem on A, pn k summability methods, which generalizes the result of Bor [5] dealing with absolute Riesz summability factors of infinite. [ABSTRACT FROM AUTHOR]

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2,Z) and let L(s,sym2f)=∑n=1∞cnn−s,ℜs>1 denote the symmetric square L-function of f. In this paper, we consider the Riesz mean of the form Dρ(x;sym2f)=L(0,sym2f)Γ(ρ+1)xρ+Δρ(x;sym2f) and derive the asymptotic formulas for ∫T−HT+HΔρk(x;sym2f)dx, when k≥3.

A theorem on φ-|A;948|k summability of infinite series, which generalises the result dealing with |N, pn|k summability of infinite series, has been proved. This theorem also contains some new results related to the |A, p|k and |C,1|k summability methods for the special cases of δ (pn), (φn), and (anv). [ABSTRACT FROM AUTHOR]

In this present paper, we have generalized a main theorem dealing with N, pn k summability of non-decreasing sequences to A, pn k summability method by using almost increasing sequences and taking normal matrices in place of weighted mean matrices. [ABSTRACT FROM AUTHOR]

In this paper, we proved a known theorem dealing with |N¯,pn|k summability factors of infinite series under weaker conditions. Also we applied this theorem to the Fourier series. [ABSTRACT FROM AUTHOR]

Extending the result of Bor(2016) and subsequently Majhi et al, a new result concerning absolute indexed Riesz Summability factors, using quasi power increasing sequence, has been established. [ABSTRACT FROM AUTHOR]

In this paper, a known theorem dealing with ∣ N¯ , pn ∣k summability factors of trigonometric Fourier series has been generalized to ∣ N¯, pn, θn ∣k summability. Some new results have also been obtained. [ABSTRACT FROM AUTHOR]

In this paper, some known results on the absolute Riesz summability factors of infinite series and Fourier series have been proved under weaker conditions. Some new and known results are also obtained. [ABSTRACT FROM AUTHOR]

We obtained necessary and sufficient conditions for the equivalence of two general summability methods. Some new and known results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, a known theorem dealing with an application of quasi power increasing sequences has extended by using a new class of increasing sequences instead of a quasi-σ-power increasing sequence. This theorem also includes some new and known results. [ABSTRACT FROM AUTHOR]

Let ∫bv and d(bv) denote the spaces of integrated and differentiated sequence spaces, which introduced by [4] and ∫bv(R) and d(bv(R)) also be matrix domain of the Riesz mean in the sequence spaces ∫bv and d(bv). In this paper, some important properties of these spaces are studied and dual spaces of the spaces ∫bv(R) and d(bv(R)) are determined. Finally, the classes (∫bv(R): Y), (d(bv(R)) : Y), (Y : ∫bv(R)) and (Y : (d(bv(R))) of infinite matrices are characterized, where Y is any given sequence space. [ABSTRACT FROM AUTHOR]

We state and prove a fuzzy analogue of a Theorem due to Móricz and Rhoades [Acta Math. Hungar. 102 (4) (2004), 279-285]. [ABSTRACT FROM AUTHOR]