Multiplication operators on Cesàro second order function spaces

Mohamed

2020

Journal of Mathematics

In this article, the necessary conditions on s-type Orlicz generalized difference sequence space to generate an operator ideal have been examined. Therefore, the s-type Orlicz generalized difference sequence space which fails to generate an operator ideal has been shown. We investigate the sufficient conditions on this sequence space to be premodular Banach special space of sequences, and the constructed pre-quasi operator ideal becomes small, simple, closed, Banach space and has eigenvalues identical with its s-numbers.

Section: Anmentioning

confidence: 99%

Orlicz Generalized Difference Sequence Space and the Linked Pre-Quasi Operator Ideal

Mohamed

2020

Journal of Mathematics

“…The multiplication maps on Cesàro sequence spaces with the Luxemburg norm explored by Komal et al [10]. _ Ilkhan et al [11] affected the multiplication maps on Cesàro second order function spaces. Recently, many authors in the literature have investigated some nonabsolute kind sequence spaces and brought recent splendid papers; for example, Mursaleen and Noman [12] defined the sequence spaces ℓ λ p and ℓ λ ∞ of nonabsolute type and proved that the spaces ℓ λ p and ℓ λ p are linearly isomorphic for 0 < p ≤ ∞, ℓ λ p is a p-normed space, and a BK -space in the cases for 0 < p < 1 and 1 ≤ p ≤ ∞ and modeled the basis for the space ℓ λ p for 1 ≤ p<∞.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Journal of Function Spaces

Dewaik

2021

Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

“…The multiplication maps on Cesàro sequence spaces with the Luxemburg norm were studied by Komal et al [20]. İlkhan et al [21] examined the multiplication maps on Cesàro second-order function spaces. Recently, many authors in the literature have considered some nonabsolute-type sequence spaces and introduced recent high-quality papers, for example, Mursaleen and Noman [22] defined the sequence space ℓ λ p and ℓ λ ∞ of nonabsolute type and proved that the spaces ℓ λ p and ℓ λ p are linearly isomorphic for 0 < p ≤ ∞, ℓ λ p is a p-normed space and a BK-space in the cases for 0 < p < 1 and 1 ≤ p ≤ ∞, and formed the basis for the space ℓ λ p for 1 ≤ p < ∞.…”

Section: Introductionmentioning

confidence: 99%

Map Ideal of Type the Domain of $r$ -Cesàro Matrix in the Variable Exponent $ℓ_{t ()}$

Journal of Function Spaces

Mohamed

2021

In this article, we define a new sequence space generated by the domain of r -Cesàro matrix in Nakano sequence space. Some geometric and topological properties of this sequence space, the multiplication maps defined on it, and the eigenvalue distributions of map ideal with s -numbers that belong to this sequence space have been examined.