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On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties

Year 2014, Volume: 3 Issue: 6, 1 - 14, 01.06.2014

Abstract

In this study, we define a new triangle matrix G ={gu,v(r, s, t)} which derived by using multiplication of weightedmean matrix G = (gnk) with triple band matrix B(r, s, t) . Also,nk(r, s, t)} which derived by using multiplication of weighted

References

  • C.-S. Wang, On N¨orlund sequence spaces, Tamkang J. Math. 9(1978) 269-274.
  • P.-N. Ng, P.-Y. Lee, Ces`aro sequence spaces of non-absolute type, Comment. Math.
  • (Prace Mat.) 20(2)(1978) 429-433.
  • E. Malkowsky, Recent results in the theory of matrix transformations in sequence
  • spaces, Mat. Vesnik 49(1997) 187-196.
  • A. M. Jarrah and E. Malkowsky, Ordinary, absolute and strong summability and
  • matrix transformations,Filomat 17(2003), 59-78
  • B. Altay, F. Ba¸sar, Some Euler sequence spaces of non-absolute type, Ukrainian
  • Math. J. 57(1)(2005) 1-17.
  • B. Altay, F. Ba¸sar, Some paranormed sequence spaces of non-absolute type derived
  • by weighted mean, J. Math. Anal. Appl. 319 (2006), 494-508.
  • H. Polat, V. Karakaya and N. S¸im¸sek, Difference sequence spaces derived by gen
  • eralized weighted mean, Appl. Math. Lett. 24(2011), no.5, 608-614.
  • B. Altay, F. Ba¸sar, Generalization of the space (p) derived by weighted mean , J.
  • Math. Anal. Appl 330 (2007) 174-185.
  • E. Malkowsky, E. Sava¸s, Matrix transformations between sequence spaces of gen
  • eralized weighted means, Appl. Math. Comput. 147(2004) 333-345.
  • M. Ba¸sarır, On some new sequence spaces and related matrix transformations, Indian J. Pure Appl. Math. 26(10) (1995) 1003-1010.
  • C. Aydın, F. Ba¸sar, On the new sequence spaces which include the spaces c0and c, Hokkaido Math. J. 33(2)(2004) 383-398.
  • F. Ba¸sar, B. Altay, M. Mursaleen, Some generalizations of the space bvpof p− bounded variation sequences, Nonlinear Anal. 68(2)(2008) 273-287.
  • M. S¸eng¨on¨ul, F. Ba¸sar, Some new Ces`aro sequence spaces of non-absolute type which include the spaces c0and c, Soochow J. Math. 31(1)(2005) 107-119.
  • B. Altay, On the space of p− summable difference sequences of order m, (1 ≤ p < ∞), Studia Sci. Math. Hungar. 43(4)(2006) 387-402.
  • H. Polat, F. Ba¸sar, Some Euler spaces of difference sequences of order m, Acta Math. Sci. 27B(2)(2007) 254-266.
  • E. Malkowsky, M. Mursaleen, S. Suantai, The dual spaces of sets of difference sequences of order m and matrix transformations, Acta Math. Sin. Eng. Ser. 23(3)(2007) 521-532.
  • F. Ba¸sar, M. Kiri¸sci, Almost convergence and generalized difference matrix, Com- put. Math. Appl. 61(2011), 602-611. [18] Demiriz, S., ¨
  • Ozdemir O., Duyar O., 2014. On some new generalized difference
  • sequence spaces of non-absolute type, arXiv:1309.3903, 2013.
  • M. Kiri¸s¸ci, F. Ba¸sar, Some new sequence spaces derived by the domain of general- ized difference matrix, Comput. Math. Appl. 60(5)(2010) 1299-1309.
  • B. Altay, F. Ba¸sar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336(1)(2007) 632- 645.
  • H. Kızmaz, On certain sequence spaces, Canad. Math. Bull. 24(2)(1981) 169-176.
  • C. Aydın, F. Ba¸sar, Some new difference sequence spaces , Appl. Math. Comput. 157(3)(2004) 677-693.
  • C. Aydın, F. Ba¸sar, Some new sequence spaces which include the spaces pand ∞, Demonstratio Math. 38(3)(2005) 641-656.
  • C. Aydın, F. Ba¸sar, Some generalizations of the sequence space ar, Iran. J. Sci. p Technol. A Sci. 30(No. A2)(2006) 175-190.
  • F. Ba¸sar, B. Altay, On the space of sequences of p− bounded variation and related matrix mappings, Ukrainian Math. J. 55(1) (2003) 136-147.
  • E. Malkowsky, M. Mursaleen, Some matrix transformations between the difference sequence spaces ∆c0(p), ∆c(p) and ∆∞(p), Filomat, 15(2001) 353-363.
  • Z. U. Ahmad, M. Mursaleen, K¨othe-Toeplitz duals of some new sequence spaces and their matrix maps, Publ. Inst. Math. (Belgrad) 42(1987) 57-61.
  • M. A. Sarıg¨ol, On difference sequence spaces, J. Karadeniz Tech. Univ. Fac. Arts. Sci. Ser. Math.-Phys. 10(1987) 63-71.
  • C¸ . Asma, R. C¸ olak, On the K¨othe-Toeplitz duals of some generalized sets of dif- ference sequences, Demonstratio Math. 33(2000) 797-803.
  • R. C¸ olak, M. Et, E. Malkowsky, Some Topics of Sequence Spaces, in: Lecture Notes in Mathematics, Fırat Univ. Press, Fırat Univ. Elazı˜g, Turkey, 2004, pp. 1-63. 2004, ISBN: 975-394-038-6.
  • M. Et, On some difference sequence spaces, Turkish J. Math. 17 (1993) 18-24.
  • A. S¨onmez, F. Ba¸sar, Generalized difference spaces of non-absolute type of con- vergent and null sequences, Abstract and Applied Analysis Volume 2012 , Article ID 435076, (2012) 20 pages.
  • M. Ba¸sarır, E. E. Kara, On the mthorder difference sequence space of generalized weighted mean and compact operators, Acta Mathematica Scientia, 33(B3)(2013), 1-18.
  • M. Ba¸sarır, E. E. Kara, On the B− difference sequence space derived by generalized weighted mean and compact operators, Journal of Mathematical Analysis and Applications, 391(2012), 67-81.
  • E. E. Kara, Some topological and geometrical properties of new Banach sequence space, Journal of Inequalities and Applications, 2013(38) (2013), 15 pages.
  • M. Ba¸sarır, E. E. Kara, On some difference sequence space of weighted means and compact operators, Annals of Functional Analysis, 2(2)(2011), 116-131.
  • E. E. Kara, M. Ba¸sarır, On compact operators and some Euler B(m)− difference sequence spaces, Journal of Mathematical Analysis and Applications, 379(2011), 499-511.
  • M. Candan, Domain of the double sequential band matrix in the classical sequence spaces, JIA, 281(1)(2012), 1-15.
  • M. Candan, Almost convergence and double sequential band matrix, Acta Math. Sci., Under Press.
  • M. Mursaleen, A.K. Noman, On the spaces of λ−convergent and bounded se- quences, Thai Journal of Mahematics, 8(2) (2010), 311-329.
  • M. Mursaleen, Abdullah K. Noman, On some new sequence spaces of non-absolute type related to the spaces pand
  • ∞I, Filomat 25:2 (2011), 33-51.
  • A. S¨onmez, Some new sequence spaces derived by the domain of the triple band matrix, Comput. Math. Appl., 62 (2011) 641-650.
  • F. Ba¸sar, Summability Theory and Its Appliactions, Bentham Science Publishers, ISBN:978-1-60805-252-3, 2011.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathe- matics Studies , Amsterdam, 85 1984.
  • M. Stieglitz, H. Tietz, Matrix transformationen von folgenr¨aumen eine ergeb- nis¨ubersicht, Math. Z. 154(1977) 1-16.
Year 2014, Volume: 3 Issue: 6, 1 - 14, 01.06.2014

Abstract

References

  • C.-S. Wang, On N¨orlund sequence spaces, Tamkang J. Math. 9(1978) 269-274.
  • P.-N. Ng, P.-Y. Lee, Ces`aro sequence spaces of non-absolute type, Comment. Math.
  • (Prace Mat.) 20(2)(1978) 429-433.
  • E. Malkowsky, Recent results in the theory of matrix transformations in sequence
  • spaces, Mat. Vesnik 49(1997) 187-196.
  • A. M. Jarrah and E. Malkowsky, Ordinary, absolute and strong summability and
  • matrix transformations,Filomat 17(2003), 59-78
  • B. Altay, F. Ba¸sar, Some Euler sequence spaces of non-absolute type, Ukrainian
  • Math. J. 57(1)(2005) 1-17.
  • B. Altay, F. Ba¸sar, Some paranormed sequence spaces of non-absolute type derived
  • by weighted mean, J. Math. Anal. Appl. 319 (2006), 494-508.
  • H. Polat, V. Karakaya and N. S¸im¸sek, Difference sequence spaces derived by gen
  • eralized weighted mean, Appl. Math. Lett. 24(2011), no.5, 608-614.
  • B. Altay, F. Ba¸sar, Generalization of the space (p) derived by weighted mean , J.
  • Math. Anal. Appl 330 (2007) 174-185.
  • E. Malkowsky, E. Sava¸s, Matrix transformations between sequence spaces of gen
  • eralized weighted means, Appl. Math. Comput. 147(2004) 333-345.
  • M. Ba¸sarır, On some new sequence spaces and related matrix transformations, Indian J. Pure Appl. Math. 26(10) (1995) 1003-1010.
  • C. Aydın, F. Ba¸sar, On the new sequence spaces which include the spaces c0and c, Hokkaido Math. J. 33(2)(2004) 383-398.
  • F. Ba¸sar, B. Altay, M. Mursaleen, Some generalizations of the space bvpof p− bounded variation sequences, Nonlinear Anal. 68(2)(2008) 273-287.
  • M. S¸eng¨on¨ul, F. Ba¸sar, Some new Ces`aro sequence spaces of non-absolute type which include the spaces c0and c, Soochow J. Math. 31(1)(2005) 107-119.
  • B. Altay, On the space of p− summable difference sequences of order m, (1 ≤ p < ∞), Studia Sci. Math. Hungar. 43(4)(2006) 387-402.
  • H. Polat, F. Ba¸sar, Some Euler spaces of difference sequences of order m, Acta Math. Sci. 27B(2)(2007) 254-266.
  • E. Malkowsky, M. Mursaleen, S. Suantai, The dual spaces of sets of difference sequences of order m and matrix transformations, Acta Math. Sin. Eng. Ser. 23(3)(2007) 521-532.
  • F. Ba¸sar, M. Kiri¸sci, Almost convergence and generalized difference matrix, Com- put. Math. Appl. 61(2011), 602-611. [18] Demiriz, S., ¨
  • Ozdemir O., Duyar O., 2014. On some new generalized difference
  • sequence spaces of non-absolute type, arXiv:1309.3903, 2013.
  • M. Kiri¸s¸ci, F. Ba¸sar, Some new sequence spaces derived by the domain of general- ized difference matrix, Comput. Math. Appl. 60(5)(2010) 1299-1309.
  • B. Altay, F. Ba¸sar, Certain topological properties and duals of the matrix domain of a triangle matrix in a sequence space, J. Math. Anal. Appl. 336(1)(2007) 632- 645.
  • H. Kızmaz, On certain sequence spaces, Canad. Math. Bull. 24(2)(1981) 169-176.
  • C. Aydın, F. Ba¸sar, Some new difference sequence spaces , Appl. Math. Comput. 157(3)(2004) 677-693.
  • C. Aydın, F. Ba¸sar, Some new sequence spaces which include the spaces pand ∞, Demonstratio Math. 38(3)(2005) 641-656.
  • C. Aydın, F. Ba¸sar, Some generalizations of the sequence space ar, Iran. J. Sci. p Technol. A Sci. 30(No. A2)(2006) 175-190.
  • F. Ba¸sar, B. Altay, On the space of sequences of p− bounded variation and related matrix mappings, Ukrainian Math. J. 55(1) (2003) 136-147.
  • E. Malkowsky, M. Mursaleen, Some matrix transformations between the difference sequence spaces ∆c0(p), ∆c(p) and ∆∞(p), Filomat, 15(2001) 353-363.
  • Z. U. Ahmad, M. Mursaleen, K¨othe-Toeplitz duals of some new sequence spaces and their matrix maps, Publ. Inst. Math. (Belgrad) 42(1987) 57-61.
  • M. A. Sarıg¨ol, On difference sequence spaces, J. Karadeniz Tech. Univ. Fac. Arts. Sci. Ser. Math.-Phys. 10(1987) 63-71.
  • C¸ . Asma, R. C¸ olak, On the K¨othe-Toeplitz duals of some generalized sets of dif- ference sequences, Demonstratio Math. 33(2000) 797-803.
  • R. C¸ olak, M. Et, E. Malkowsky, Some Topics of Sequence Spaces, in: Lecture Notes in Mathematics, Fırat Univ. Press, Fırat Univ. Elazı˜g, Turkey, 2004, pp. 1-63. 2004, ISBN: 975-394-038-6.
  • M. Et, On some difference sequence spaces, Turkish J. Math. 17 (1993) 18-24.
  • A. S¨onmez, F. Ba¸sar, Generalized difference spaces of non-absolute type of con- vergent and null sequences, Abstract and Applied Analysis Volume 2012 , Article ID 435076, (2012) 20 pages.
  • M. Ba¸sarır, E. E. Kara, On the mthorder difference sequence space of generalized weighted mean and compact operators, Acta Mathematica Scientia, 33(B3)(2013), 1-18.
  • M. Ba¸sarır, E. E. Kara, On the B− difference sequence space derived by generalized weighted mean and compact operators, Journal of Mathematical Analysis and Applications, 391(2012), 67-81.
  • E. E. Kara, Some topological and geometrical properties of new Banach sequence space, Journal of Inequalities and Applications, 2013(38) (2013), 15 pages.
  • M. Ba¸sarır, E. E. Kara, On some difference sequence space of weighted means and compact operators, Annals of Functional Analysis, 2(2)(2011), 116-131.
  • E. E. Kara, M. Ba¸sarır, On compact operators and some Euler B(m)− difference sequence spaces, Journal of Mathematical Analysis and Applications, 379(2011), 499-511.
  • M. Candan, Domain of the double sequential band matrix in the classical sequence spaces, JIA, 281(1)(2012), 1-15.
  • M. Candan, Almost convergence and double sequential band matrix, Acta Math. Sci., Under Press.
  • M. Mursaleen, A.K. Noman, On the spaces of λ−convergent and bounded se- quences, Thai Journal of Mahematics, 8(2) (2010), 311-329.
  • M. Mursaleen, Abdullah K. Noman, On some new sequence spaces of non-absolute type related to the spaces pand
  • ∞I, Filomat 25:2 (2011), 33-51.
  • A. S¨onmez, Some new sequence spaces derived by the domain of the triple band matrix, Comput. Math. Appl., 62 (2011) 641-650.
  • F. Ba¸sar, Summability Theory and Its Appliactions, Bentham Science Publishers, ISBN:978-1-60805-252-3, 2011.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathe- matics Studies , Amsterdam, 85 1984.
  • M. Stieglitz, H. Tietz, Matrix transformationen von folgenr¨aumen eine ergeb- nis¨ubersicht, Math. Z. 154(1977) 1-16.
There are 55 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Osman Duyar This is me

Serkan Demiriz This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 3 Issue: 6

Cite

APA Duyar, O., & Demiriz, S. (2014). On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties. Journal of New Results in Science, 3(6), 1-14.
AMA Duyar O, Demiriz S. On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties. JNRS. June 2014;3(6):1-14.
Chicago Duyar, Osman, and Serkan Demiriz. “On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties”. Journal of New Results in Science 3, no. 6 (June 2014): 1-14.
EndNote Duyar O, Demiriz S (June 1, 2014) On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties. Journal of New Results in Science 3 6 1–14.
IEEE O. Duyar and S. Demiriz, “On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties”, JNRS, vol. 3, no. 6, pp. 1–14, 2014.
ISNAD Duyar, Osman - Demiriz, Serkan. “On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties”. Journal of New Results in Science 3/6 (June 2014), 1-14.
JAMA Duyar O, Demiriz S. On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties. JNRS. 2014;3:1–14.
MLA Duyar, Osman and Serkan Demiriz. “On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties”. Journal of New Results in Science, vol. 3, no. 6, 2014, pp. 1-14.
Vancouver Duyar O, Demiriz S. On Some New Generalized Di®erence Sequence Spaces and Their Topological Properties. JNRS. 2014;3(6):1-14.


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