Research Article
BibTex RIS Cite

A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX

Year 2015, Volume: 3 Issue: 2, 62 - 76, 01.10.2015

Murat Candan , Gülsen Kılınç

Abstract

This paper presents the generalized Riesz sequence space rq( b Fp u ) which is formed all sequences whose Rqu b F-transforms are in the space `(p), where b F is a Fibonacci matrix. - - and -duals of the newly described sequence space have been given in addition to some topological properties of its. Also, it has been established the basis of rq( b Fp u ). Finally, we have been described a matrix class on the sequence space. Results obtained are more general and more comprehensive than presented up to now.

Keywords

Paranormed sequence space Fibonacci numbers alpha- beta- and gamma-duals and matrix mappings

References

  • [1] B. Altay, On the space of p􀀀summable di erence sequences of order m, (1  p < 1), Stud. Sci. Math. Hungar., 43(4)(2006), 387{402.
  • [2] B. Altay, F. Basar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 26(2002), 701{715.
  • [3] B. Altay, F. Basar, Some paranormed sequence spaces of non-absolute type derived by weighted mean, J. Math. Anal. Appl., 319(2)(2006), 494{508.
  • [4] B. Altay, F. Basar, Generalization of the sequence space `(p) derived by weighted mean, J. Math. Anal. Appl., 330(2007), 174{185.
  • [5] B. Altay, F. Basar, The matrix domain and the ne spectrum of the di erence operator  on the sequence space `p, (0 < p < 1), Commun. Math. Anal., 2(2)(2007), 1{11.
  • [6] B. Altay, F. Basar, On the ne spectrum of the generalized di erence operator B(r; s) over the sequence c0 and c, Int. J. Math. Sci., 18(2008), 3005{3013.
  • [7] B. Altay, F. Basar, M. Mursaleen, On the Euler sequence spaces which include the spaces `p and `1 I, Inform. Sci., 176(10)(2006), 1450{1462.
  • [8] C. Aydn, F. Basar, Some new sequence spaces which include the spaces `p and `1, Demonstratio Math., 38(3)(2005), 641-656.
  • [9] C. Aydn, F. Basar, Some generalizations of the sequence spaces arp, Iran J. Sci. Technol. Trans. A. Sci., 30A(2)(2006), 175{190.
  • [10] F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, xi+405 pp., _Istanbul, (2012), ISB:978-1-60805-252-3.
  • [11] F. Basar, B. Altay, On the space of sequences of p􀀀bounded variation and related matrix mappings, Ukrainian Math.J., 55(1)(2003), 136{147.
  • [12] F. Basar, M. Kirisci, Almost convergence and generalized di erence matrix, Comput. Math. Appl., 61(3) (2011), 602{611.
  • [13] M. Basarr, Paranormed Cesaro di erence sequence space and related matrix transformation, Doga Tr. J. Math., 15(1991), 14{19.
  • [14] M. Basarr, On the generalized Riesz B-di erence sequence spaces, Filomat., 24(4)(2010), 35{52.
  • [15] M. Basarr, F. Basar, E. E. Kara, On the Fibonacci Di erence Null and Convergent Sequences, arXiv:1309.0150.
  • [16] M. Basarr, E. E. Kara, On some di erence sequence spaces of weighted means and compact operators, Ann. Funct. Anal., 2(2)(2011), 116{131.
  • [17] M. Basarr, E. E. Kara, On compact operators on the Riesz Bm􀀀di erence sequence space, Iran J. Sci. Technol. Trans., 35A(4)(2011), 279{285.
  • [18] M. Basarr, E. E. Kara, On compact operators on the Riesz Bm􀀀di erence sequence space-II, Iran J. Sci. Technol. Trans., 36A(3)(2012), 371{376.
  • [19] M. Basarr, E. E. Kara, On the B􀀀di erence sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391(2012), 67{81.
  • [20] M. Basarr, E. E. Kara, On the mth order di erence sequence space of generalized weighted mean and compact operator, Acta. Math. Sci., 33B(3)(2013), 1{18.
  • [21] M. Basarr, M. Kaykc, On the generalized Bth􀀀Riesz di erence sequence space and betaproperty, J. Inequal. Appl., ID 385029, (2009), 18pp.
  • [22] M. Basarr, M.  Ozturk, On the Riesz diference sequence space, Rend. Circ. Mat. Palermo., 57(2008), 377{389.
  • [23] M. Basarr, M.  Ozturk, On some Generalized Bm􀀀di erence Riesz Sequence Spaces and Uniform Opial Property, J. Inequal. Appl., ID 485730 (2011), 17 pp.
  • [24] M. Candan, Some new sequence spaces de ned by a modulus function and an in nite matrix in a seminormed space, J. Math. Anal., 3(2) (2012), 1{9.
  • [25] M. Candan, Domain of the double sequential band matrix in the classical sequence spaces, J. Inequal. Appl., 281(2012), 15 pp.
  • [26] M. Candan, Almost convergence and double sequential band matrix, Acta. Math. Sci., 34B(2)(2014), 354{366.
  • [27] M. Candan, A new sequence space isomorphic to the space `(p) and compact operators, J. Math. Comput. Sci., 4, No: 2(2014), 306{334.
  • [28] M. Candan, Domain of the double sequential band matrix in the spaces of convergent and null sequences, Adv. Di erence Edu., (2014)163, 18 pp.
  • [29] M. Candan, Some new sequence spaces derived from the spaces of bounded, convergent and null sequences, Int. J. Mod. Math. Sci., 12(2)(2014), 74-87.
  • [30] M. Candan, Vector-Valued FK-spaces de ned by a modulus function and an in nite matrix, Thai J. Math., 12(1)(2014),155-165.
  • [31] M. Candan, A new aproach on the spaces of generalized Fibonacci di erence null and convergent sequences, Math. terna., 1(5)(2015), 191{210.
  • [32] M. Candan, A. Gunes, Paranormed sequence space of non-absolute type founded using generalized di erence matrix, Proc. Natl. Acad. Sci., India Sect. A Phys. Sci., 85(2)(2015), 269{276.
  • [33] M. Candan, E. E. Kara, A study on topological and geometrical characteristics of new Banach sequence spaces, Gulf J. of Math., 3(4)(2015), 67-84.
  • [34] M. Candan, K. Kayaduman, Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Brithish J. Math. Comput. Sci., 7(2)(2015), 150{167.
  • [35] M. Candan, _I. Solak, On some Di erence Sequence Spaces Generated by In nite Matrices, Int. J. Pure Appl. Math., 25(1)(2005), 79{85.
  • [36] M. Candan, _I. Solak, On New Di erence Sequence Spaces Generated by In nite Matrices, Int. J. Sci. and Tecnology., 1(1)(2006), 15{17.
  • [37] B. Choudhary, S. K Mishra, On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. Pure Appl. Math., 245(1993), 291{301.
  • [38] R. C olak, M. Et, Malkowsky E, Some Topics of Sequence Spaces, Lecture Notes in Mathematics, Frat Univ, Elazg, Turkey,(2004), pp. 1{63, Frat Univ, Press, ISBN: 975-394-038-6.
  • [39] R. C olak, M. Et, On some generalized di erence sequence spaces and related matrix transformations, Hokkaido Math. J., 26(3)(1997), 483{492.
  • [40] S. Demiriz, C. C akan, Some topolojical and geometrical properties of a new di erence sequence space, Abstr. Appl. Anal., doi:10.1155/2011/213878, 14 pp.
  • [41] M. Et, Generalized Cesaro di erence sequence spaces of non-absolute type involving lacunary sequence spaces, Appl. Math. Comput., 219(17)(2013), 9372{9376.
  • [42] M. Et, M. Isk, On pa-dual spaces of generalized di erence sequence spaces, Appl. Math. Lett., 25(10)(2012), 1486{1489.
  • [43] A. H. Ganie, N. A. Sheikh, New type of paranormed sequence space of non-absolute type and a matrix transformation, Int, J of Mod, Math, Sci., 8(2)(2013), 196{211.
  • [44] K. Goswin, G. Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223{238.
  • [45] C. G. Lascarides, I. J. Maddox, Matrix transformations between some classes of sequences, Proc. Cambridge Philos. Soc., 68(1970), 99{104.
  • [46] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 38(2013).
  • [47] E. E. Kara, M. Basarr, M. Mursaleen, Compact operators on the Fibonacci di erence sequence spaces lp( b F) and l1( b F), 1st International Eurasian Conf. on Math.Sci.and Appl. Prishtine-Kosovo, (2012), September 3-7.
  • [48] E. E. Kara, M.  Ozturk, M. Basarr, Some topological and geometric properties of generalized Euler sequence spaces, Math., Slovaca, 60(3)(2010), 385{398.
  • [49] H. Kzmaz, On certain sequence spaces, Canad. Math. Bull., 24(2)(1981), 169{176.
  • [50] M. Kirisci, Almost convergence and generalized weighted mean I, AIP Conf. Proc. vol, 1470(2012), pp. 191{194.
  • [51] M. Kirisci, On the spaces of Euler almost null and Euler almost convergent sequences, Commun. Fac. Sci. Univ., Ankara, 2(2013), 85{100.
  • [52] M. Kirisci, Almost convergence and generalized weighted mean II, J. Inequal. Appl., ID 193,(2014), 13pp.
  • [53] M. Kirisci, F. Basar, Some new sequence spaces derived by the domain of generalized di erence matrix, Comput. Math. Appl., 60(5)(2010), 1299{1309.
  • [54] S. Konca, M. Basarr, Generalized di erence sequence spaces associated with a multiplier sequence on a real n􀀀normed space, J. Inequal. Appl., ID 335(2013), 12 pp.
  • [55] S. Konca, M. Basarr, On some spaces of almost lacunary convergent sequences derived by Riesz mean and weighted almost lacunary statistical convergence in a real n􀀀normedspace, J, Inequal. Appl., ID 81(2014), 11 pp.
  • [56] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., Oxford, 18(2)(1967), 345{355.

Year 2015, Volume: 3 Issue: 2, 62 - 76, 01.10.2015

Murat Candan , Gülsen Kılınç

Abstract

References

  • [1] B. Altay, On the space of p􀀀summable di erence sequences of order m, (1  p < 1), Stud. Sci. Math. Hungar., 43(4)(2006), 387{402.
  • [2] B. Altay, F. Basar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 26(2002), 701{715.
  • [3] B. Altay, F. Basar, Some paranormed sequence spaces of non-absolute type derived by weighted mean, J. Math. Anal. Appl., 319(2)(2006), 494{508.
  • [4] B. Altay, F. Basar, Generalization of the sequence space `(p) derived by weighted mean, J. Math. Anal. Appl., 330(2007), 174{185.
  • [5] B. Altay, F. Basar, The matrix domain and the ne spectrum of the di erence operator  on the sequence space `p, (0 < p < 1), Commun. Math. Anal., 2(2)(2007), 1{11.
  • [6] B. Altay, F. Basar, On the ne spectrum of the generalized di erence operator B(r; s) over the sequence c0 and c, Int. J. Math. Sci., 18(2008), 3005{3013.
  • [7] B. Altay, F. Basar, M. Mursaleen, On the Euler sequence spaces which include the spaces `p and `1 I, Inform. Sci., 176(10)(2006), 1450{1462.
  • [8] C. Aydn, F. Basar, Some new sequence spaces which include the spaces `p and `1, Demonstratio Math., 38(3)(2005), 641-656.
  • [9] C. Aydn, F. Basar, Some generalizations of the sequence spaces arp, Iran J. Sci. Technol. Trans. A. Sci., 30A(2)(2006), 175{190.
  • [10] F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, xi+405 pp., _Istanbul, (2012), ISB:978-1-60805-252-3.
  • [11] F. Basar, B. Altay, On the space of sequences of p􀀀bounded variation and related matrix mappings, Ukrainian Math.J., 55(1)(2003), 136{147.
  • [12] F. Basar, M. Kirisci, Almost convergence and generalized di erence matrix, Comput. Math. Appl., 61(3) (2011), 602{611.
  • [13] M. Basarr, Paranormed Cesaro di erence sequence space and related matrix transformation, Doga Tr. J. Math., 15(1991), 14{19.
  • [14] M. Basarr, On the generalized Riesz B-di erence sequence spaces, Filomat., 24(4)(2010), 35{52.
  • [15] M. Basarr, F. Basar, E. E. Kara, On the Fibonacci Di erence Null and Convergent Sequences, arXiv:1309.0150.
  • [16] M. Basarr, E. E. Kara, On some di erence sequence spaces of weighted means and compact operators, Ann. Funct. Anal., 2(2)(2011), 116{131.
  • [17] M. Basarr, E. E. Kara, On compact operators on the Riesz Bm􀀀di erence sequence space, Iran J. Sci. Technol. Trans., 35A(4)(2011), 279{285.
  • [18] M. Basarr, E. E. Kara, On compact operators on the Riesz Bm􀀀di erence sequence space-II, Iran J. Sci. Technol. Trans., 36A(3)(2012), 371{376.
  • [19] M. Basarr, E. E. Kara, On the B􀀀di erence sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391(2012), 67{81.
  • [20] M. Basarr, E. E. Kara, On the mth order di erence sequence space of generalized weighted mean and compact operator, Acta. Math. Sci., 33B(3)(2013), 1{18.
  • [21] M. Basarr, M. Kaykc, On the generalized Bth􀀀Riesz di erence sequence space and betaproperty, J. Inequal. Appl., ID 385029, (2009), 18pp.
  • [22] M. Basarr, M.  Ozturk, On the Riesz diference sequence space, Rend. Circ. Mat. Palermo., 57(2008), 377{389.
  • [23] M. Basarr, M.  Ozturk, On some Generalized Bm􀀀di erence Riesz Sequence Spaces and Uniform Opial Property, J. Inequal. Appl., ID 485730 (2011), 17 pp.
  • [24] M. Candan, Some new sequence spaces de ned by a modulus function and an in nite matrix in a seminormed space, J. Math. Anal., 3(2) (2012), 1{9.
  • [25] M. Candan, Domain of the double sequential band matrix in the classical sequence spaces, J. Inequal. Appl., 281(2012), 15 pp.
  • [26] M. Candan, Almost convergence and double sequential band matrix, Acta. Math. Sci., 34B(2)(2014), 354{366.
  • [27] M. Candan, A new sequence space isomorphic to the space `(p) and compact operators, J. Math. Comput. Sci., 4, No: 2(2014), 306{334.
  • [28] M. Candan, Domain of the double sequential band matrix in the spaces of convergent and null sequences, Adv. Di erence Edu., (2014)163, 18 pp.
  • [29] M. Candan, Some new sequence spaces derived from the spaces of bounded, convergent and null sequences, Int. J. Mod. Math. Sci., 12(2)(2014), 74-87.
  • [30] M. Candan, Vector-Valued FK-spaces de ned by a modulus function and an in nite matrix, Thai J. Math., 12(1)(2014),155-165.
  • [31] M. Candan, A new aproach on the spaces of generalized Fibonacci di erence null and convergent sequences, Math. terna., 1(5)(2015), 191{210.
  • [32] M. Candan, A. Gunes, Paranormed sequence space of non-absolute type founded using generalized di erence matrix, Proc. Natl. Acad. Sci., India Sect. A Phys. Sci., 85(2)(2015), 269{276.
  • [33] M. Candan, E. E. Kara, A study on topological and geometrical characteristics of new Banach sequence spaces, Gulf J. of Math., 3(4)(2015), 67-84.
  • [34] M. Candan, K. Kayaduman, Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Brithish J. Math. Comput. Sci., 7(2)(2015), 150{167.
  • [35] M. Candan, _I. Solak, On some Di erence Sequence Spaces Generated by In nite Matrices, Int. J. Pure Appl. Math., 25(1)(2005), 79{85.
  • [36] M. Candan, _I. Solak, On New Di erence Sequence Spaces Generated by In nite Matrices, Int. J. Sci. and Tecnology., 1(1)(2006), 15{17.
  • [37] B. Choudhary, S. K Mishra, On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. Pure Appl. Math., 245(1993), 291{301.
  • [38] R. C olak, M. Et, Malkowsky E, Some Topics of Sequence Spaces, Lecture Notes in Mathematics, Frat Univ, Elazg, Turkey,(2004), pp. 1{63, Frat Univ, Press, ISBN: 975-394-038-6.
  • [39] R. C olak, M. Et, On some generalized di erence sequence spaces and related matrix transformations, Hokkaido Math. J., 26(3)(1997), 483{492.
  • [40] S. Demiriz, C. C akan, Some topolojical and geometrical properties of a new di erence sequence space, Abstr. Appl. Anal., doi:10.1155/2011/213878, 14 pp.
  • [41] M. Et, Generalized Cesaro di erence sequence spaces of non-absolute type involving lacunary sequence spaces, Appl. Math. Comput., 219(17)(2013), 9372{9376.
  • [42] M. Et, M. Isk, On pa-dual spaces of generalized di erence sequence spaces, Appl. Math. Lett., 25(10)(2012), 1486{1489.
  • [43] A. H. Ganie, N. A. Sheikh, New type of paranormed sequence space of non-absolute type and a matrix transformation, Int, J of Mod, Math, Sci., 8(2)(2013), 196{211.
  • [44] K. Goswin, G. Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180(1993), 223{238.
  • [45] C. G. Lascarides, I. J. Maddox, Matrix transformations between some classes of sequences, Proc. Cambridge Philos. Soc., 68(1970), 99{104.
  • [46] E. E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Inequal. Appl., 38(2013).
  • [47] E. E. Kara, M. Basarr, M. Mursaleen, Compact operators on the Fibonacci di erence sequence spaces lp( b F) and l1( b F), 1st International Eurasian Conf. on Math.Sci.and Appl. Prishtine-Kosovo, (2012), September 3-7.
  • [48] E. E. Kara, M.  Ozturk, M. Basarr, Some topological and geometric properties of generalized Euler sequence spaces, Math., Slovaca, 60(3)(2010), 385{398.
  • [49] H. Kzmaz, On certain sequence spaces, Canad. Math. Bull., 24(2)(1981), 169{176.
  • [50] M. Kirisci, Almost convergence and generalized weighted mean I, AIP Conf. Proc. vol, 1470(2012), pp. 191{194.
  • [51] M. Kirisci, On the spaces of Euler almost null and Euler almost convergent sequences, Commun. Fac. Sci. Univ., Ankara, 2(2013), 85{100.
  • [52] M. Kirisci, Almost convergence and generalized weighted mean II, J. Inequal. Appl., ID 193,(2014), 13pp.
  • [53] M. Kirisci, F. Basar, Some new sequence spaces derived by the domain of generalized di erence matrix, Comput. Math. Appl., 60(5)(2010), 1299{1309.
  • [54] S. Konca, M. Basarr, Generalized di erence sequence spaces associated with a multiplier sequence on a real n􀀀normed space, J. Inequal. Appl., ID 335(2013), 12 pp.
  • [55] S. Konca, M. Basarr, On some spaces of almost lacunary convergent sequences derived by Riesz mean and weighted almost lacunary statistical convergence in a real n􀀀normedspace, J, Inequal. Appl., ID 81(2014), 11 pp.
  • [56] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., Oxford, 18(2)(1967), 345{355.
There are 56 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Murat Candan

Gülsen Kılınç

Publication Date October 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Candan, M., & Kılınç, G. (2015). A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX. Konuralp Journal of Mathematics, 3(2), 62-76.
AMA Candan M, Kılınç G. A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX. Konuralp J. Math. October 2015;3(2):62-76.
Chicago Candan, Murat, and Gülsen Kılınç. “A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 62-76.
EndNote Candan M, Kılınç G (October 1, 2015) A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX. Konuralp Journal of Mathematics 3 2 62–76.
IEEE M. Candan and G. Kılınç, “A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX”, Konuralp J. Math., vol. 3, no. 2, pp. 62–76, 2015.
ISNAD Candan, Murat - Kılınç, Gülsen. “A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX”. Konuralp Journal of Mathematics 3/2 (October 2015), 62-76.
JAMA Candan M, Kılınç G. A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX. Konuralp J. Math. 2015;3:62–76.
MLA Candan, Murat and Gülsen Kılınç. “A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 62-76.
Vancouver Candan M, Kılınç G. A DIFFERENT LOOK FOR PARANORMED RIESZ SEQUENCE SPACE DERIVED BY FIBONACCI MATRIX. Konuralp J. Math. 2015;3(2):62-76.
 Download Cover Image
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.