Abstract. We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
The deferred Cesáro transformation, which has useful properties not possessed by the Cesáro transformation, was considered by RP Agnew in 1932. The aim of this paper is to give a generalization of deferred Cesáro transformations by taking account of some well-known transformations and to handle some of their properties as well. On the other hand, we shall consider the approximation by the generalized deferred Cesáro means in a generalized Hölder metric and present some applications of the approach concerning some sequence classes. MSC: Primary 40Gxx; 41A25; secondary 42A10
In this paper we shall present results related to trigonometric approximation of functions belonging to the weighted generalized Lipschitz class by the (C 1 · T ) matrix means of their Fourier series. The results of Lal in [8] will be extended to a more general summability method. Moreover, we present the results on degree of approximation to conjugates of functions belonging to a weighted generalized Lipschitz class by the (C 1 · T ) matrix means of their conjugate Fourier series.
In this work, we shall give the degree of approximation for functions belonging to Hölder class by matrix summability method of multiple Fourier series in the Hölder metric.
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