NEW TYPE OF ALMOST CONVERGENCE
Abstract
In [1] for a given sequence $(\lambda_{n})$ with $\lambda_{n}< \lambda_{n+1} \rightarrow \infty$ a new summability method $C_{\lambda}$ was introduced which generalizes the classical Ces\`{a}ro method. In this paper, we introduce some new almost convergence and almost statistical convergence definitions for sequences which generalize the classical almost convergence and almost statistical convergence.
Keywords
Full Text:
PDFReferences
D. H. Armitage and I. J. Maddox: A new type of Cesaro mean, Analysis,
, no. 1-2, (1989), 195-204.
C. Belen and S. A. Mohiuddine: Generalized weighted statistical convergence
and application, Appl. Math. Comput. 219 (2013) 9821-9826.
N. L. Braha, H. M. Srivastava and S. A. Mohiuddine: A Korovkin's type
approximation theorem for periodic functions via the statistical summability of the
generalized de la Vallee Poussin mean, Appl. Math. Comput. 228 (2014) 162-169.
J. Connor: The statistical and strong p-Cesaro convergence of sequences, Analysis
(1988), 47-63.
J. Connor: On strong matrix summability with respect to a modulus and statis-
tical convergence, Canad. Math. Bull. 32 (1989), 194-198.
J. Connor: Two valued measures and summability, Analysis 10 (1990), 373-385.
H. Fast: Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
J. A. Fridy: On statistical convergence, Analysis 5 (1985), 301-313.
J. A. Fridy: and H. I. Miller: A matrix characterization of statistical
convergence, Analysis 11 (1991), 55-66.
J. A. Fridy and C. Orhan: Lacunary statistical summability, J. Math. Anal.
Appl. 173 (1993), 497-504.
J. A. Fridy and C. Orhan: Lacunary statistical convergence, Pacific J. Math.
(1993), 43-51.
C. Goffman and G. M. Petersen: Submethods of regular matrix summability
methods, Canad. J. Math. 8, (1956) 400-56.
G. Lorentz: A contribution to the theory of divergent sequences, Acta Math.
(1948) 167-190.
U. Kadak and S. A. Mohiuddine: Generalized statistically almost convergence
based on the difference operator which includes the (p; q)-Gamma function and
related approximation theorems, Results Math. (2018) 73:9.
I. J. Maddox: A new type of convergence, Math. Proc. Cambridge Philos. Soc.
(1978), 61-64.
I. J. Maddox: Statistical convergence in locally convex spaces, Math. Proc.
Cambridge Philos. Soc. 104 (1988), 141-145.
I. J. Maddox: Sequence spaces defined by a modulus, Math. Proc. Cambridge
Philos. Soc.,100 (1986), 161-166.
S. A. Mohiuddine and B. A. S. Alamri: Generalization of equi-
statistical convergence via weighted lacunary sequence with associated Korovkin
and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas
Fis. Nat. Ser. A Math. RACSAM 113(3) (2019), 1955-1973.
S. A. Mohiuddine: An application of almost convergence in approximation
theorems, Appl. Math. Lett. 24 (2011) 1856-1860.
S. A. Mohiuddine, and A. Alotaibi: Weighted almost convergence and related
infinite matrices, J. Inequal. Appl. (2018) 2018:15.
T. Salat: On statistically convergent sequences of real numbers, Math. Slovaca,
(1980), 139-150.
S. A. Mohiuddine, B. Hazarika and M. A. Alghamdi: Ideal relatively uni-
form convergence with Korovkin and Voronovskaya types approximation theorems,
Filomat 33(14) (2019) 4549-4560.
H. Nakano: Concave modulus, J. Math. Soc. Japon. 5 (1953), 29-49
J. A. Osikiewicz: Equivalence results for Cesaro submethods, Analysis, 20(1)
(2000), 35-43.
W. H. Ruckle: FK spaces in which the sequence of coordinate vectors is bounded,
Canad. J. Math. 25 (1973), 973-978.
E. Savas and F. Nuray: On $sigma$-statistically convergence and lacunary $sigma$-
statistically convergence, Math. Slovaca, 43(3) (1993), 309-315.
I. J. Schoenberg: The integrability of certain functions and related summability
methods, Amer. Math. Monthly, 66 (1959), 361-375.
W. F. Steele: Summability of infinite sequences by submatrix methods, Ph.D.
Dissertation, Univ. of Pitstsburg, Pittsburg, Pennsylvania 1961.
DOI: https://doi.org/10.22190/FUMI200304056N
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)