In this paper, we study the Lehmer’s type congruences for lacunary harmonic sums.

A well known theorem states as follows :' Let ni < n2 <. . ., nk+1 / nk > A > 1 be an infinite sequence of real numbers and S (ak + bk) a divergent series satisfying k=1 Then denotes the Lebesgue measure of the set in question. It seems likely that the Theorem remains true if it is not assumed that the n k are integers. On the other hand if nk ,f-n,.-1 is an arbitrary sequence of integers it is...

in this paper, under the condition that $k$ is concave, we characterize lacunary series in $q_{k}$ spaces. we improve a result due to h. wulan and k. zhu.

Lacunary polyoxometalates (POMs) are negatively charged metal–oxo clusters, formally obtained from plenary topologies via fragment removal. Owing to the removal, lacunary POMs archetypes rich in nucleophilic terminal oxo ligands, making them suitable for post-synthetic coordination with various heterometals. Trilacunary heteropolytungstates (hetero-POTs) based on bowl-shaped {W9O30} framework i...

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

In this paper we study the concept of lacunary statistical convergent triple sequences in probabilistic normed spaces and prove some basic properties.

In summability theory, de la Vallée-Poussin’s mean is first used to define the (V, λ)-summability by Leindler [9]. Malkowsky and Savaş [14] introduced and studied some sequence spaces which arise from the notion of generalized de la ValléePoussin mean. Also the (V, λ)-summable sequence spaces have been studied by many authors including [6] and [20]. Recently, there has been a lot of interest in...