Abstract
In this paper we introduce a new concept for Riesz almost lacunary $\Gamma^{3}$ sequence spaces strong $P-$ convergent to zero with respect to an Musielak-Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary $\Gamma^{3}$ sequence spaces and also some inclusion theorems are discussed.
Highlights
Is called the complementary function of a Musielak-Orlicz function f
The four dimensional matrix A is said to be RH-regular if it maps every bounded P − convergent sequence into a P − convergent sequence with the same P − limit
The assumption of boundedness was made because a triple sequence spaces which is P − convergent is not necessarily bounded
Summary
Is called the complementary function of a Musielak-Orlicz function f. Let f be an Musielak-Orlicz function and p = (pmnk) be any factorable triple sequence of positive real numbers. Let f be an Musielak-Orlicz function, p = pmnk be any factorable triple sequence of positive real numbers and and qmnk, qmnk and qmnk be sequences of positive numbers and Qr = q111 + · · · qrst, Qs = q111 · · · qrst and Qt = q112 · · · qrst, If we choose qmnk = 1, qmnk = 1 and qmnk = 1 for all m, n and k, we obtain the following sequence spaces.
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