Lacunary strong convergence of difference sequences with respect to a modulus function
Keyword(s):
A sequence ? = (kr) of positive integers is called lacunary if k0 = 0, 0 < kr < kr+1 and hr = kr ? kr-1 ? ? as r ? ?. The intervals determined by ? are denoted by Ir = (kr-1, kr]. Let ? be the set of all sequences of complex numbers and f be a modulus function. Then we define N?(?m, f) = {x ? ?: lim 1/hr ? f(|?m xk -l|)=0 for some l} r k?Ir N?0(?m, f) = {x ? ?: lim 1/hr ? f(|?m xk|)=0} r k?Ir N??(?m, f) = {x ? ?: sup 1/hr ? f(|?m xk|)< ?} r k?Ir where ?xk = xk - xk+1, ?mxk = ?m-1xk - ?m-1xk+1 and m is a fixed positive integer. In this study we give various properties and inclusion relations on these sequence spaces.
Keyword(s):
Keyword(s):
2018 ◽
Vol 107
(02)
◽
pp. 272-288
2014 ◽
Vol 0
(0)
◽