Absolute Nörlund summability factors of power series and Fourier series
The definition of lacunary strongly convergence is extended to the definition of lacunary strong -convergence with respect to invariant mean when is an infinite matrix and is a strictly positive sequence. We study some properties and inclusion relations.
The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.
In the paper, we prove two theorems on summability, , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.
In this paper a theorem on summability factors, which generalizes a theorem of Mishra and Srivastava [MS] on summability factors, has been proved.