In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr）...In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.展开更多
In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not t...In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not there is a constant term in f,and we obtain two redefined Bohr inequalities in Un.Finally,we redefine the Bohr inequality of the odd and even terms of the analytic function f so as to obtain conclusions for two different higher-dimensional alternating series.展开更多
In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α an...In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.展开更多
文摘In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.
基金supported by Guangdong Natural Science Foundations(2021A1515010058)。
文摘In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not there is a constant term in f,and we obtain two redefined Bohr inequalities in Un.Finally,we redefine the Bohr inequality of the odd and even terms of the analytic function f so as to obtain conclusions for two different higher-dimensional alternating series.
文摘In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.
