Absolute │A; δ │k and │A; γ; δ│k Summability for n-tupled Triangle Matrices

2020 ◽  
Vol 3 (2) ◽  
pp. 27-34
Author(s):  
Smita Sonker ◽  
Alka Munjal ◽  
Lakshmi Narayan Mishra
Keyword(s):  
Real Number ◽  
Bounded Operator ◽  
Sufficient Conditions ◽  
Summability Method ◽  
Sequence Spaces ◽  
Minimal Set

In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ank ; δ) & (Ank ; γ; δ): Generalized summability method │A; δ │k & │A; γ; δ│k have been applied for determining the sufficient conditions, where k ≥ 1; δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.

On absolute summability for double triangle matrices

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Ekrem Savaş ◽  
Hamdullah Şevli
Keyword(s):  
Bounded Operator ◽  
Sufficient Conditions ◽  
Absolute Summability ◽  
Infinite Matrix ◽  
Double Sequences ◽  
Weighted Mean ◽  
Minimal Set ◽  
Principal Diagonal ◽  
Summability Methods ◽  
Necessary And Sufficient

AbstractA lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a double triangle T to be a bounded operator on ; i.e., T ∈ B () for the sequence space defined below. As special summability methods T we consider weighted mean and double Cesàro, (C, 1, 1), methods. As a corollary we obtain necessary and sufficient conditions for a double triangle T to be a bounded operator on the space of double sequences of bounded variation.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

scholarly journals A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

1995 ◽  
Vol 18 (4) ◽  
pp. 681-688 ◽  
Author(s):  
B. Choudhary ◽  
S. K. Mishra
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Necessary And Sufficient

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

scholarly journals Localization and summability of multiple Hermite series

1997 ◽  
Vol 20 (1) ◽  
pp. 61-74
Author(s):  
G. E. Karadzhov ◽  
E. E. El-Adad
Keyword(s):  
Sufficient Conditions ◽  
Summability Method ◽  
Dimensional Case ◽  
Localization Principle ◽  
Riesz Summability ◽  
Lebesgue Set ◽  
Hermite Series

The multiple Hermite series inRnare investigated by the Riesz summability method of orderα>(n−1)/2. More precisely, localization theorems for some classes of functions are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended to then-dimensional case. In particular, for these classes of functions the localization principle and summability on the Lebesgue set are established.

scholarly journals Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Uğur Kadak ◽  
Hakan Efe
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
General Linear ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
Complex Field ◽  
Infinite Matrices ◽  
The Matrix ◽  
Necessary And Sufficient

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the fieldC*and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets overC*to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples.

scholarly journals A unified common fixed point theorem for a family of mappings

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 759-769
Author(s):  
Vijay Dalakoti ◽  
Ravindra Bisht ◽  
R.P. Pant ◽  
Mahesh Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Minimal Set ◽  
Contractive Type ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

scholarly journals On Certain Sequence Spaces

1981 ◽  
Vol 24 (2) ◽  
pp. 169-176 ◽  
Author(s):  
H. Kizmaz
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Necessary And Sufficient

AbstractIn this paper define the spaces l∞(Δ), c(Δ), and c0(Δ), where for instance l∞(Δ) = {x=(xk):supk |xk -xk + l|< ∞}, and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l∞(Δ) or c(Δ) into l∞ or c, and investigate related questions.

Masked factorable matrices

2002 ◽  
Vol 132 (1) ◽  
pp. 245-254
Author(s):  
Gord Sinnamon
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Necessary And Sufficient ◽  
Factorable Matrices

The class of masked factorable matrices is introduced and simple necessary and sufficient conditions are given for matrices in the class to represent bounded transformations between Lebesgue sequence spaces.

On generalized Fibonacci difference sequence spaces and compact operators

2021 ◽  
pp. 2250116
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Mikail Et
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Band Matrix ◽  
Matrix Formula ◽  
Necessary And Sufficient ◽  
Matrix Mappings ◽  
Difference Sequence Spaces

In this paper, we introduce Fibonacci backward difference operator [Formula: see text] of fractional order [Formula: see text] by the composition of Fibonacci band matrix [Formula: see text] and difference operator [Formula: see text] of fractional order [Formula: see text] defined by [Formula: see text] and introduce sequence spaces [Formula: see text] and [Formula: see text] We present some topological properties, obtain Schauder basis and determine [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the spaces [Formula: see text] and [Formula: see text] We characterize certain classes of matrix mappings from the spaces [Formula: see text] and [Formula: see text] to any of the space [Formula: see text] [Formula: see text] [Formula: see text] or [Formula: see text] Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces [Formula: see text] and [Formula: see text]

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