On certain generalized matrix methods of convergence in (ℓ)-groups
-
Pratulananda Das
and
Ekrem Savas
Abstract
We introduce a convergence of weight g: ℕ → [0, ∞) where g(n) → ∞ and n/g(n) ↛ 0 with respect to a summability matrix method A for sequences (which generalizes the notion of A-convergence of order α, 0 < α ≤ 1 [BOCCUTO, A.—DAS, P.: On matrix methods of convergence of order (α) in (ℓ)-groups, Filomat 29 (2015), 2069–2077] in a (ℓ)-group. We prove some basic results including a Cauchy-type criterion. Finally a closedness result for the space of such convergent sequences is proved.
Acknowledgement
The first author is thankful to TUBITAK for granting Visiting Scientist position for one month and to SERB, DST, New Delhi for granting a research project No. SR/S4/MS: 813/13 during the tenure of which this work was done.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Outer measure on effect algebras
- Hamiltonian ordered algebras and congruence extension
- Automorphism groups with some finiteness conditions
- Only finitely many Tribonacci Diophantine triples exist
- Abundant semigroups with a *-normal idempotent
- Stability results for fractional differential equations with state-dependent delay and not instantaneous impulses
- Monotonicity results for delta fractional differences revisited
- M-Cantorvals of Ferens type
- Comparison of ψ-porous topologies
- On certain generalized matrix methods of convergence in (ℓ)-groups
- Some applications of first-order differential subordinations
- Hankel determinant for a class of analytic functions involving conical domains defined by subordination
- Nonoscillation and exponential stability of the second order delay differential equation with damping
- Positive solutions of perturbed nonlinear hammerstein integral equation
- Ricci solitons on 3-dimensional cosymplectic manifolds
- Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups
- The super socle of the ring of continuous functions
- On the internal approach to differential equations 2. The controllability structure
- Finiteness of the discrete spectrum in a three-body system with point interaction
- On a subclass of Bazilevic functions
