Asymptotically Double Lacunary Statistically Equivalent Sequences of Interval Numbers

 

Ayhan Esi

Adiyaman University

Shyamal Debnath

Subrata Saha 

Tripura University

India

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 ABSTRACT

In this paper we have introduced the concept ofasymptotically double lacunary statistically equivalent of interval numbers and strong asymptotically double lacunary statistically equivalent ofinterval numbers. We have investigated the relations related to these spaces.

Subjclass [2010] : 40C05, 46A45.

Keywords : asymptotically, Lacunary, Interval number.

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REFERENCES

[1]    A. Esi, Strongly almost convergence and statistically almost convergence of interval numbers, Sci. Magna, 7 (2), pp. 117-122, (2011).

[2]    A. Esi, Lacunary sequence spaces of interval numbers, Thai J. Math, 10 (2), pp. 445-451, (2012).

[3]    A. Esi, A-Sequence spaces of interval numbers, Appl. Math. Inf. Sci, 8 (3), pp. 1099-1102, (2014).

[4]    A. Esi, A new class of interval numbers, J. Qafqaz Univ., Math. and Comp. Sci, 33, pp. 98-102, (2012).

[5]    A. Esi, Double lacunary sequence spaces of double sequence of interval numbers, Proyec. J. Math, 31 (1), pp. 297-306, (2012).

[6]    A. Esi, Statistical and lacunary statistical convergence of interval numbers in topological groups, Acta Scien. Techno, 36 (3), pp. 491-495, (2014).

[7]    A. Esi and N.Braha, On asymptotically A-statistical equivalent sequences of interval numbers, Acta Scien. Techno, 35 (3), pp. 515-520, (2013).

[8]    A. Esi and A. Esi, Asymptotically lacunary statistically equivalent sequences of interval numbers, International J. Math. and Appl, 1 (1), pp. 43-48, (2013).

[9]    A. Esi and B. Hazarika, Some ideal convergence of double/\ -interval number sequences defined by Orlicz function, Global J. Math. Anal, 1 (3), pp. 110-116, (2013).

[10]    A. R. Freedman, J. J. Sember and M. Raphael, Some cesaro type summability, Proc. London Math. Soc., 37 (3), pp. 508-520, (1978).

[11]    H. Cakalli, A study on statistical convergence, Funct. Anal. Approx. Comput. 1 (2), pp. 19-24, (2009).

[12]    H. Fast, Sur la convergence statistique, Colloq. Math. 2, pp. 241-244, (1951) .

[13]    H. I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Am. Math. Soc. 347 (5), pp. 1811-1819, (1995).

[14]    I. J. Maddox, On strong almost convergence, Math. Proc. Camb. Phi-los. Soc. 85 (2), pp. 345-350, (1979).

[15]    I. J. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon. 66, pp. 361-375, (1951).

[16]    J. A. Fridy, On statistical convergence, Analysis, 5, pp. 301-313, (1985).

[17]    J. A. Fridy and C. Orhan, Lacunary statistical convergence. Pacific J. Math. 160 (1), pp. 43-51, (1993).

[18]    Kuo-Ping Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematics, 18(2), pp. 219-233, (2002).

[19]    M. Marouf,, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci., 16(4), pp. 755-762, (1993).

[20]    M. Mursaleen and O. H.Edely, Statistical convergence of double se-quences, J. Math. Anal. Appl. 288 (1), pp. 223-231, (2003).

[21]    M. §engonül and A. Eryilmaz, On the sequence spaces of interval num-bers, Thai J. Math, 8 (3), pp. 503-510, (2010).

[22]    P. S. Dwyer, Linear Computation, New York, Wiley, (1951).

[23]    P. S. Dwyer, Erros of Matrix Computation, Simultaneous Equations and Eigenvalues, Nat. Bureau Standarts, Appl. Math. Series, 29, pp. 49-58, (1953).

[24]    P. S. Fischer, Automatic Propagated and Round-off Error Analysis, paper presented at the 13th national meeting of the Association for Computing Machinary, (1958).

[25]    R. E. Moore, Automatic Error Analysis in Digital Computation, LSMD-48421, Lockheed Missiles and Space Company, (1959).

[26]    R. E. Moore and C. T. Yang, Theory of an Interval Algebra and Its Application to Numeric Analysis, RAAG Memories II, Gaukutsu Bunken Fukeyu-kai, Tokyo, (1962).

[27]    R. F. Patterson, On asymptotically statistically equivalent sequences, Demonstratio Math., 36 (1), pp. 149-153, (2003).

[28]    R. F. Patterson and E Savas, On asymptotically lacunary statistical equivalent sequences, Thai J. Math., 4(2), pp. 267-272, (2006).

[29]    S. Debnath, A. J. Datta and S. Saha, Regular Matrix of Interval Numbers based on Fibonacci Numbers, Afr. Mat., 26(7), pp. 1379-1385, (2015).

[30]    S. Debnath, B. Sarma and S. Saha, On some sequence spaces of interval vectors, Afr. Mat., 26(5), pp. 673-678, (2015).

[31]    S. Debnath and S. Saha, On Statistically Convergent Sequence Spaces ofInterval Numbers, Proceedings ofIMBIC, 3, pp. 178-183, (2014).

Ayhan Esi

Department of Mathematics Adiyaman university,

Turkey

e-mail : aesi23@hotmail.com

Shyamal Debnath

Department of Mathematics

Tripura University,

India

e-mail : shyamalnitamath@gmail.com and

Subrata Saha

Department of Mathematics Tripura University,

India

e-mail : subratasaha2015@gmail.com

Received : June 2016. Accepted : October 2016