PARANORMED SPACES OF ABSOLUTE LUCAS SUMMABLE SERIES AND MATRIX OPERATORS

Fadime Gökçe

DOI Number
https://doi.org/10.22190/FUMI200602020G
First page
259
Last page
274

Abstract


The aim of this paper is to introduce the absolute series space $\left\vert \mathcal{L}^{\phi }(r,s)\right\vert (\mu )$ as the the set of all series summable by the absolute Lucas method, and to give its topological and algebraic structure such as $FK-$space, duals and Schauder basis. Also,  certain matrix operators on this space are characterized.

Keywords

Absolute summability, Lucas numbers, matrix transformations, Maddox space, sequence spaces, bounded operators

Full Text:

PDF

References


bibitem{AB2006} {sc B. Altay {rm and} F. Bac{s}ar}: textit{Some paranormed Riesz

sequence spaces of non-absolute type}. Southeast Asian Bull. Math. {bf 30(5)} (2006), 591-608.

bibitem{BD2018} {sc H. Bilgin {rm and} S. Demiriz}: textit{Some Algebraic And Topological Properties

Of New Lucas Difference Sequence Spaces}. Turk. J. Math. {bf 10 }(Special Issue: Proceedings of ICMME 2018), 144-152.

bibitem{B1985}{sc H. Bor}: textit{On $leftvert overline{N},p_{n}rightvert _{k}$ summability factors of infinite series}. Tamkang J. Math. {bf 16} (1985), 13-20.

bibitem{DC2012}{sc S. Demiriz {rm and} C.c{C}akan}: textit{Some New Paranormed Difference Sequence

Spaces And Weighted Core}. Comput. Math. with Appl. {bf 64(6)} (2012), 1726-1739.

bibitem{F1957} {sc T. M. FLett}: textit{On an extension of absolute summability

and some theorems of Littlewood and Paley}. Proc. Lond. Math. Soc. {bf 7}(1957), 113-141.

bibitem{GS2018a} {sc F. G"{o}kc{c}e {rm and} M. A. Sari g"{o}l}: textit{A new series space $leftvert overline{N}_{p}^{theta}rightvert left( muright)$ and matrix transformations with applications}. Kuwait J. Sci. {bf 45(4)} (2018), 1-8.

bibitem{GS2018b} {sc F. G"{o}kc{c}e {rm and} M. A. Sari g"{o}l}:

textit{Generalization of the space $l(p)$ derived by absolute Euler

summability and matrix operators}. J. Inequal. Appl. {bf 2018 (1)} (2018), 133.

bibitem{GS2019} {sc F. G"{o}kc{c}e {rm and} M. A. Sari g"{o}l}:

textit{Generalization of the absolute Ces`{a}ro space and some matrix

transformations}. Numer. Funct. Anal. Optim. {bf 40(9)} (2019), 1039-1052.

bibitem{GS2020} {sc F. G"{o}kc{c}e {rm and} M. A. Sari g"{o}l}: textit{Some

matrix and compact operators of the absolute Fibonacci series spaces}.

Kragujevac J. Math. {bf 44(2)} (2020), 273--286.

bibitem{IDK2019} {sc M. Ilkhan, S. Demiriz {rm and} E. E. Kara}: textit{A New Paranormed Sequence

Space Defined by Euler Totient Matrix}. Karaelmas Sci. Eng. J.

{bf 9(2)} (2019), 277-282.

bibitem{JM2003} {sc A. M. Jarrah {rm and} E. Malkowsky}: textit{Ordinary absolute

and strong summability and matrix transformations}. Filomat. {bf 17} (2003), 59-78.

bibitem{GE1993}{sc K. G. Grosse-Erdmann}: textit{Matrix transformations

between the sequence spaces of Maddox}. J. Math. Anal. Appl. {bf180} (1993), 223-238.

bibitem{KI2016} {sc E. E. Kara {rm and} M. Ilkhan }: textit{Some properties of

generalized Fibonacci sequence spaces}. Linear Multilinear Algebra. {bf 64(11)} (2016), 2208-2223.

bibitem{KD2015} {sc E. E. Kara {rm and} S. Demiriz}: textit{Some New Paranormed Difference Sequence

Spaces Derived By Fibonacci Numbers}. Miskolc Math. Notes. {bf 16(2)} (2015), 907-923.

bibitem{KK2018} {sc M. Karakac{s} {rm and} A. M. Karakac{s}}: textit{A study on

Lucas difference sequence spaces $l_{p}(hat{E}(r,s))$ and $l_{infty }(%

hat{E}(r,s))$}. Maejo Int. J. Sci. Technol. {bf 12(1)} (2018), 70-78.

bibitem{KNP2011} {sc V. Karakaya, A. K. Noman {rm and} H. Polat}: textit{On

paranormed $lambda $-sequence spaces of non-absolute type}. Math. Comp. Model. {bf 54(5)} (2011), 1473-1480.

bibitem{K2011} {sc T. Koshy}: textit{Fibonacci and Lucas numbers with

applications}. 51, John Wiley and Sons, 2011.

bibitem{M1969} {sc I. J. Maddox}: textit{Some properties of paranormed sequence

spaces}. J. London Math. Soc. {bf 2} (1969), 316-322.

bibitem{M1968} {sc I. J. Maddox}: textit{Paranormed sequence spaces generated

by infinite matrices}. Math. Proc. Cambridge Philos. Soc. {bf 64} (1968), 335-340.

bibitem{M1967} {sc I. J. Maddox}: textit{Spaces of strongly summable sequences}.

Q. J. Math. {bf 18} (1947), 345-355.

bibitem{MR2007} {sc E. Malkowsky {rm and} V. Rakocevic}: textit{On matrix domains

of triangles}. Appl. Math. Comput. {bf 189(2)} (2007), 1146-1163.

bibitem{MR2000} {sc E. Malkowsky {rm and} V. Rakocevic}: textit{An introduction

into the theory of sequence space and measures of noncompactness}. Zbornik radova (Beogr). {bf 9(17)} (2000), 143-234

bibitem{M2013} {sc M. Mursaleen}: textit{Applied Summability Methods}. Springer, Heidelberg, 2013.

bibitem{MS1975} {sc R. N. Mohapatra {rm and} M. A. Sar{i }g"{o}l}: textit{On

matrix operators on the series spaces $leftvert bar{N}_{p}^{theta

}rightvert _{k}$}. Ukrainian Math. J. {bf 69(11)} (2018), 1524-1533.

bibitem{S2016} {sc M. A. Sar{i }g"{o}l}: textit{Spaces of Series Summable by

Absolute Ces$grave{a}$ro and matrix operators}. Comm. Math Appl. {bf 7(1)} (2016), 11-22.

bibitem{S2013} {sc M. A. Sar{i }g"{o}l}: textit{An inequality for matrix

operators and its applications}. J. Class. Anal. {bf 2} (2013), 145-150.

bibitem{S2011} {sc M. A. Sar{i }g"{o}l}: textit{Matrix transformations on

fields of absolute weighted mean summability}. Studia Sci. Math. Hungar. {bf 48(3)} (2011), 331-341.

bibitem{S2010} {sc M. A. Sar{i }g"{o}l}: textit{On the local properties of

factored Fourier series}. Appl. Math. Comput. {bf 216(11)} (2010), 3386-3390.

bibitem{SU1992} {sc W. T. Sulaiman}: textit{On summability factors of infinite

series}. Proc. Amer. Math. Soc. {bf 115} (1992), 313- 317.

bibitem{W1984} {sc A. Wilansky}: textit{Summability Through Functional Analysis, Mathematics Studies}. 85. North Holland , Amsterdam, 1984.




DOI: https://doi.org/10.22190/FUMI200602020G

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)