We note that the continued fraction expansion of a lacunary formal power series is a folded continued fraction with monomial partial quotients, and with the property that its convergents have denominators that are the sums of distinct monomials, that is, they are polynomials with coefficients 0, 1, and −1 only. Our results generalise, simplify and refine remarks of a previous note ‘Convergents ...

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

The sequence X = {Ark } of fuzzy numbers is statistically convergent to the fuzzy number 3(o provided that for each e ~ 0 lim l{the number ofk~e} = 0. n In this paper we study a related concept of convergence in which the set {k: k<~n} is replaced by {k: kr-1 -~k<~kr} for some lacunary sequence {k~}. Also we introduce the concept of lacunary statistically Cauchy sequence and show...

In this paper we purpose to define the notions of lacunary statistical convergence and lacunary statistically Cauchy in random 2-normed spaces and proved some interesting results for these concepts in this set up.

In this paper we introduce the concepts of double lacunary strongly convergence and double lacunary statistical convergence of double interval numbers. We prove some inclusion relations and study some of their properties. Subjclass [2000] : 40C05,40J05, 46A45.

For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by ω-limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiés hyperbolic functions of higher order and lacunary functions play an important role f...