In this article, we investigate the summability of formal power series solutions in time a certain class inhomogeneous partial differential equations with polynomial semilinearity, and variable coefficients. particular, give necessary sufficient conditions for k-summability given direction, where k is positive rational number entirely determined by linear part equation. These generalize ones au...

We quantify the elementary Borel–Cantelli Lemma by higher moments of overlap count statistic in terms weighted summability probabilities. Applications include mean deviation frequencies Strong Law and Iterated Logarithm.

We prove that allKK-homology classes of the stable (and unstable) Ruelle algebra a Smale space have explicit Fredholm module representatives ...

Various investigators such as Khan ([1-4]), Khan and Ram [5], Chandra [6,7], Leindler [8], Mishra et al. [9], Mishra [10], Mittal et al. [11], Mittal, Rhoades and Mishra [12], Mittal and Mishra [13], Rhoades et al. [14] have determined the degree of approximation of 2π-periodic signals (functions) belonging to various classes Lip   , Lip r   Lip     , r t  , and W L of functions throu...

Mittal and Rhoades (1999–2001) andMittal et al. (2006) have initiated the studies of error estimates En( f ) through trigonometric Fourier approximations (TFA) for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of a function ̃ f , conjugate to a periodic function f belonging to the weighted W(Lp,ξ(t))-class (p...

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...

It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...

Wedetermine the degree of approximation of conjugate of a function belonging to Lip(ξ(t),p) class by matrix summability means of a conjugate series of a Fourier series. 2000 Mathematics Subject Classification. 42B05, 42B08.

In this paper we deal with a main theorem on the local property of ∣∣N, pn∣∣k, k ≥ 1 summability of factored Fourier series, which generalizes some known results. Mathematics Subject Classification: 40D15, 40G99, 42A24, 42B15