"lambda" - STATISTICAL SUPREMUM - INFIMUM AND "lambda" - STATISTICAL CONVERGENCE

Abstract

In this paper, we are going to define λ-statistical supremum and λ-statistical infimum for real valued sequencex = (xn) n∈N by considering λ-statistical upper and lower bounds, respectively. After giving some basic properties of these new notations, then we will give a necessary and sufficient condition for to existance of λ-statistical convergence of the real valued sequence.

Weighted Statistical Limit Supremum-Infimum

“…In this section, weighted analogue of statistical upper and statistical lower bound, introduced and studied in [2,3], will be given by considering g density.…”

$\mu$-statistical convergence and the space of functions $\mu$-stat continuous on the segment

“…Let ε > 0 be an arbitrary number. Let n 0 ∈ N be such that 1 n 0 < ε. Then for all x ∈ x 0 , 1 n 0 we have…”

“…The second direction treated these kinds of convergence in various mathematical structures (see [1][2][3][4][5][6]12,13,[22][23][24]27,28,31,39,41]). In [26,34,36], the statistical convergence was generalized for double sequences, and the properties of this convergence were studied.…”

CERTAIN ASPECTS OF Xrst(G)-CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

“…Later on, statistical convergence was further investigated and worked from the sequence space point of view by Fridy [24,25], Šalát [34], Tripathy [37,38], Connor [16], and many others [3,4,5,6,26].…”