ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION

Vakeel A. Khan; Hira Fatıma; Sameera A. A. Abdullah; Kamal M. A. S. Alshlool

ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION

Abstract

The sequence space BV_(σ )was introduced and studied by Mursaleen [Houston J. Math. 9, 505-509 (1983; Zbl 0542.40003)]. The main aim of this paper is to study some new double sequence spaces of invariant means defined by ideal and modulus function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.

Keywords

References

Ahmad,Z.U., and Mursaleen,M.(1988), “An application of Banach limits,” Proc.Amer. Math. soc 103(1), 244-246. Banach,S.(1986), “Theorie des operations lineaires,” Warszawa, (1932)103, 244-246.
Fast,H.(1951), “Sur la convergence statistique,” Colloq. Math. 2, 241-244.
Fridy,J.A.(1985), “On statistical convergence,” Analysis. 5, 301-313.
Gramsch,B.(1967), “Die Klasse metrisher linearer Raume L(Á),” Math. Ann. 171, 61-78.
Habil, E.D., 2006, “Double sequences and double series,” The Islamic University Journal,Series of Natural Studies and Engineering, vol. 14, pp, 1-33.
Hazarika, B., Karan, T. and Singh,B.K. (2014), “Zweier Ideal convergent sequence space defined by Orlicz function,” Journal of mathematics and com- puter science 8, 307-318
Khan,V.A.(2008), “On a new sequence space defined by Orlicz function,” Communications de la Faculté des Sciences de l'Université d'Ankara SériesA1.57, 25-33.
Khan, V. A. and Ebadullah, K. (2013), “On some new convergent sequence space,” Mathematics, Aeterna 3(2)151-159.

Khan, V. A. and Ebadullah, K. (2012), “On a new I-convergent sequence space,” Analysis 32, 199-208.
Khan, V.A., Fatima, H., Abdullaha, S.A.A., Khan, M.D. (2016), “On a New BVσ-I-Convergent Double Sequence Spaces,” Theory and Application of mathematics and computer science 6 (2), 187-197.
Khan,V.A., Ebadullah,K.(2012), “I-convergent sequences spaces defined by sequence of moduli,” Journal of Mathematical and Computational Science 2 (2), 265-273.
Khan, V.A, Esi, A. and Shafiq, M.(2014) , “On some BV_σ I-convergent sequence spaces Defined by modulus function ,” Global Journal of Mathematical Analysis, 2(2) 17-27.
King, J.P.(1966), “Almost summable Sequences,” Proc.Amer. Math. soc.17, 1219-1225.
Kayaduman, K., and Sengönül, M. (2014), “Some New Type Sigma Convergent Sequence Spaces and Some New Inequalities,” Scientific world journal 589765.
Kostyrko,P. ,Ŝalát, T. and Wilczyński,W.(2000), “I convergence,” Real Analysis Exchange. 26(2), 669-686.
Kostyrko,P.,Mańaj, M. and Salát,T., “Statistical convergence and I-convergence,” Real Analysis Exchange.
KÄothe, G. (1970) , “Topological Vector spaces.1.” Springer, Berlin.
Lorentz, G.G. (1948), “A contribution to the theory of divergent series,” Acta Math, 80, 167-190.
Mursaleen, M.(1983), “On some new invariant matrix methods of summability,” The Quart. J. Math., 34(133), 77-86.
Mursaleen, M.(1983), “Matrix transformation between some new sequence spaces,” Houston J. Math.9, 505-509.
Maddox, I.J.(1970), “Elements of Functional Analysis,” Cambridge University Press.
Maddox, I.J.(1968), “Paranormed sequence spaces generated by infinite matrices,” Math. Proc. Cambridge Philos. Soc. 64,335340.
Maddox, I.J.(1986), “Sequence spaces defined by a modulus,” Math. Camb. Phil. Soc.100, 161-166.
Nakano, H.(1951), “Modular sequence spaces.” Proc. Jpn. Acad. Ser. A Math. Sci. 27, 508512.
Raimi, R.A.(1963), “Invariant means and invariant matrix methods of summability,” Duke J. Math.30, 81-94.
Ruckle, W.H.(1968), “On perfect Symmetric BK-spaces”, Math.Ann. 175, 121-126.
Ruckle, W.H.(1967), “Symmetric coordinate spaces and symmetric bases”, Canad.J.Math. 19, 828-838.
Ruckle, W.H.(1973), “FK-spaces in which the sequence of coordinate vectors is bounded,” Canad.J. Math.25 (5) 973-975.
Saláat, T., Tripathy, B.C. and Ziman, M. (2004), “On some properties of I-convergence,” Tatra Mt. Math. Publ. 28, 279-286.
Salát, T., Tripathy, B.C and Ziman, M.(2005) , “On I-convergence field,” Ital. J. Pure Appl. Math. 17, 45-54.
Tripathy, B.C and Hazarika, B.(2009), “Paranorm I-convergent sequence spaces,” Math. Slovaca. 59(4), 485-494.
Tripathy, B.C., Hazarika, B.(2008), “I-convergent sequence spaces associated with multiplier sequences,” Math. Ineq. Appl. 11(3), 543548.
Tripathy,B.C and Hazarika,B.(2011), “Some I-Convergent sequence spaces defined by Orlicz function,” Acta Mathematicae Applicatae Sinica.27(1),149-154.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Vakeel A. Khan This is me
0000-0002-4132-0954
India

Hira Fatıma This is me
0000-0003-0407-6072
India

Sameera A. A. Abdullah This is me
0000-0003-4094-2978
India

Kamal M. A. S. Alshlool This is me
0000-0003-0029-2405
India

Publication Date

December 1, 2017

Submission Date

May 4, 2017

Acceptance Date

September 7, 2017

Published in Issue

Year 2017 Volume: 35 Number: 4

IZ

https://izlik.org/JA46CF43CH

Cite

RIS / Bibtex

APA

Khan, V. A., Fatıma, H., Abdullah, S. A. A., & Alshlool, K. M. A. S. (2017). ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. Sigma Journal of Engineering and Natural Sciences, 35(4), 695-706. https://izlik.org/JA46CF43CH

AMA

1.Khan VA, Fatıma H, Abdullah SAA, Alshlool KMAS. ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. SIGMA. 2017;35(4):695-706. https://izlik.org/JA46CF43CH

Chicago

Khan, Vakeel A., Hira Fatıma, Sameera A. A. Abdullah, and Kamal M. A. S. Alshlool. 2017. “ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION”. Sigma Journal of Engineering and Natural Sciences 35 (4): 695-706. https://izlik.org/JA46CF43CH.

EndNote

Khan VA, Fatıma H, Abdullah SAA, Alshlool KMAS (December 1, 2017) ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. Sigma Journal of Engineering and Natural Sciences 35 4 695–706.

IEEE

[1]V. A. Khan, H. Fatıma, S. A. A. Abdullah, and K. M. A. S. Alshlool, “ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION”, SIGMA, vol. 35, no. 4, pp. 695–706, Dec. 2017, [Online]. Available: https://izlik.org/JA46CF43CH

ISNAD

Khan, Vakeel A. - Fatıma, Hira - Abdullah, Sameera A. A. - Alshlool, Kamal M. A. S. “ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION”. Sigma Journal of Engineering and Natural Sciences 35/4 (December 1, 2017): 695-706. https://izlik.org/JA46CF43CH.

JAMA

1.Khan VA, Fatıma H, Abdullah SAA, Alshlool KMAS. ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. SIGMA. 2017;35:695–706.

MLA

Khan, Vakeel A., et al. “ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION”. Sigma Journal of Engineering and Natural Sciences, vol. 35, no. 4, Dec. 2017, pp. 695-06, https://izlik.org/JA46CF43CH.

Vancouver

1.Vakeel A. Khan, Hira Fatıma, Sameera A. A. Abdullah, Kamal M. A. S. Alshlool. ON SOME NEW I-CONVERGENT DOUBLE SEQUENCE SPACES OF INVARIANT MEANS DEFINED BY IDEAL AND MODULUS FUNCTION. SIGMA [Internet]. 2017 Dec. 1;35(4):695-706. Available from: https://izlik.org/JA46CF43CH