APPLICATIONS OF INFINITE MATRICES IN NON-NEWTONIAN CALCULUS FOR PARANORMED SPACES AND THEIR TOEPLITZ DUALS

Kuldip Raj, Charu Sharma

DOI Number
10.22190/FUMI1704527R
First page
527
Last page
549

Abstract


The main purpose of this paper is to construct some difference sequence
spaces over the geometric complex numbers for an infinite matrix and Museilak-Orlicz
function. We also make an effort to study some inclusion relations, topological and
geometric properties of these spaces. An endeavor has been made to prove that these
are Banach spaces. Furthermore, we compute the $\alpha$-, $\beta$-, $\gamma$-dual of these spaces.


Keywords

geometric difference, Orlicz function, paranorm space, geometric complex numbers, non-Newtonian calculus, Köthe- Toeplitz duals

Keywords


Geometric difference; Orlicz function; paranorm space; geometric complex numbers; non-Newtonian calculus; K\"{o}the- Toeplitz duals.

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References


A. Ostrowski: Solution of Equations and Systems of Equations. Academic Press, New York, 1966.

E. B. Saff and R. S. Varga: On incomplete polynomials II. Pacific J. Math. 92 (1981), 161–172.

A. E. Bashirov, E. M. Kurpnar, and A. Ozyapc, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.

C . A. Bektas, M. Et and R. C olak, Generalized dierence sequence spaces and their dual spaces, J. Math. Anal. Appl., 292 (2004), 423-432.

K. Boruah, B. Hazarika, and M. Et, Generalized Geometric Dierence Sequence Spaces and its duals, arXiv:1603.09497v1 [math.FA] 31 March 2016.

A. F. Cakmak and F. Basar, On the classical sequence spaces and non-newtonian calculus, J. Inequal. Appl., 2012.

M. Et, Y. Altin, B. Choudhary and B. C. Tripathy, On some classes of sequences dened by sequences of Orlicz functions, Math. Inequal. Appl., 9(2) (2006), 335-342.

A. Esi, B. C. Tripathy and B. Sarma, On some new type generalized dierence sequence spaces, Math. Slovaca, 57 (2007), 475-482.

D. J. H. Garling, The - and -duality of sequence spaces, Proc. Camb. Phil. Soc., 63 (1967), 963-981.

J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.

P. Korus, On 2-strong convergence of numerical sequences revisited, Acta Math. Hungar., 148 (2016), 222-227.

P. Korus, On the uniform convergence of double sine series with generalized monotone coecients, Period. Math. Hungar., 63 (2011), 205-2014.

P. Korus, On the uniform convergence of special sine integrals, Acta Math. Hungar., 133 (2011), 82-91.

G. Kothe and O. Toplitz, Linear Raume mit unendlichen koordinaten und Ring unendlichen Matrizen, J. F. Reine u. angew Math., 171 (1934), 193-226.

M. Et and A. Esi, On Kothe-Toeplitz duals of generalized dierence sequence spaces, Bull. Malays. Math. Sci. Soc., 23 (2000), 25-32.

M. Et and R. C olak, On generalized dierence sequence spaces, Soochow J. Math., 21 (1995), 377-386.

M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, 1972.

M. Grossman, Bigeometric Calculus, Archimedes Foundation Box 240, Rockport,Mass, USA, 1983.

H. Kzmaz, On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169-176.

L. Maligranda, Orlicz spaces and interpolation, Seminars in Mathematics, 5, Polish Academy of Science, (1989).

I. J. Maddox, Innite Matrices of Operators, Lecture notes in Mathematics, 786, Springer-Verlag(1980).

M. Mursaleen, Sunil K. Sharma, S. A. Mohiuddine, A. Kilicman, New dierence sequence spaces dened by Musielak-Orlicz function, Abstr. Appl. Anal. 2014, Art. ID 691632, 9 pp. 46B20.

M. Mursaleen, S. A. Mohiuddine, Convergence methods for double sequences and applications, Springer, New Delhi, 2014. x+171 pp.

J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer Verlag, (1983).

K. Raj, A. Azimhan and K. Ashirbayev, Some generalized dierence sequence spaces of ideal convergence and Orlicz functions, J. Comput. Anal. Appl. 22 (2017), 52-63.

K. Raj and C. Sharma, Applications of strongly convergent sequences to Fourier series by means of modulus functions, Acta Math. Hungar., 150(2016), 396-411.

K. Raj and A. Kilicman, On certain generalized paranormed spaces, J. Inequal. Appl. (2015), 2015: 37.

K. Raj and S. Pandoh, Generalized lacunary strong Zweier Convergent Sequence spaces, Toyama Math. J. 38 (2016), 9-33.

S. Tekin and F. Basar, Certain sequence spaces over the non-Newtonian complex eld, Abst. and Appl. Anal., (2013), Article ID 739319, 11 pages.

C. Turkmen and F. Basar, Some basic results on the sets of sequences with geometric calculus, Commun. Fac. Sci. Univ. Ank. Series A1, 61 (2012), 17-34.

B.C. Tripathy, A. Esi and B. Tripathy, On a new type of generalized dierence Cesaro sequence spaces, Soochow J. Math., 31 (2005), 333-340.

B. C. Tripathy and A. Esi, A new type of dierence sequence spaces, Int. J. Sci. Tech., 1 (2006), 11-14.

A. Wilansky, Summability through functional analysis, North-Holland Math. Stud., 85 (1984).




DOI: https://doi.org/10.22190/FUMI1704527R

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