Deferred Cesàro summability and statistical convergence for double sequences of sets

The main purpose of this paper is introduced the concept of deferred Cesàro mean in the Wijsman sense for double sequences of sets and then presented the concepts of strongly deferred Cesàro summability and deferred statistical convergence in the Wijsman sense for double sequences of sets. Also, investigate the relationships between these concepts and then to prove some theorems associated with the concepts of deferred statistical convergence in the Wijsman sense for double sequences of sets is purposed.

Cesàro and Abel ergodic theorems for integrated semigroups

Let {S(t)}t ≥ 0 be an integrated semigroup of bounded linear operators on the Banach space 𝒳 into itself and let A be their generator. In this paper, we consider some necessary and sufficient conditions for the Cesàro mean and the Abel average of S(t) converge uniformly on ℬ(𝒳). More precisely, we show that the Abel average of S(t) converges uniformly if and only if 𝒳 = ℛ(A) ⊕ 𝒩(A), if and only if ℛ(Ak) is closed for some integer k and ∥ λ 2 R(λ, A) ∥ → 0 as λ→ 0+, where ℛ(A), 𝒩(A) and R(λ, A), be the range, the kernel, the resolvent function of A, respectively. Furthermore, we prove that if S(t)/t 2 → 0 as t → 1, then the Cesàro mean of S(t) converges uniformly if and only if the Abel average of S(t) is also converges uniformly.

Some subordination involving polynomials induced by lower triangular matrices

The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

The spectrum generated by s-numbers and pre-quasi normed Orlicz-Cesáro mean sequence spaces

In this article, we study some topological properties of the multiplication operator on Orlicz-Cesáro mean sequence spaces equipped with the pre-quasi norm and the pre-quasi operator ideal constructed by this sequence space and s-numbers.