Research Article
BibTex RIS Cite

Year 2020, Volume: 9 Issue: 4, 1537 - 1544, 25.12.2020

Murat Karakaş Hacer Dönmez

Abstract

References

  • [1] Vajda S. 1989. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Dover Publications Inc., New York, 1-190.
  • [2] Kalman D., Mena R. 2003. The Fibonacci Numbers: Exposed. Mathematics Magazine, 76 (3): 167-181.
  • [3] Candan M., Kara E.E. 2015. A Study on Topological and Geometrical Characteristics of new Banach Sequence Spaces. Gulf Journal of Mathematics, 3 (4): 67-84.
  • [4] Kılınç G., Candan M. 2017. Some Generalized Fibonacci Difference Spaces Defined by a Sequence of Modulus Functions. Facta Universitatis, Series: Mathematics and Informatics, 32 (1): 95-116.
  • [5] Kara E.E. 2013. Some Topological and Geometrical Properties of New Banach Sequence Spaces. Journal of Inequalities and Applications, 2013 (38): 1-15.
  • [6] Kara E.E., Başarır M. 2012. An Application of Fibonacci Numbers into Infinite Toeplitz Matrices. Caspian Journal of Mathematics Sciences, 1 (1): 1-6.
  • [7] Karakaş M. 2015. A New Regular Matrix Defined by Fibonacci Numbers and Its Applications. BEU Journal of Science, 4 (2): 205-210.
  • [8] Karakaş M., Karakaş A.M. 2018. A Study on Lucas Difference Sequence Spaces and . Maejo International Journal of Science and Technology, 12 (1): 70-78.
  • [9] Karakaş M., Akbaş T., Karakaş A.M. 2019. On the Lucas Difference Sequence Spaces Defined by Modulus Function. Applications and Applied Mathematics, 14 (1): 235-244.
  • [10] Fast H. 1951. Sur La Convergence Statistique. Colloquium Mathematicum, 2: 241-244.
  • [11] Steinhaus H. 1951. Sur la Convergence Ordinaire et La Convergence Asymptotique. Colloquium Mathematicum, 2: 73–74.
  • [12] Fridy J.A. 1985. On Statistical Convergence. Analysis, 5: 301–313.
  • [13] Connor J.S. 1988. The Statistical and Strong p-Cesàro Convergence of Sequences. Analysis, 8: 47–63.
  • [14] Çınar M., Karakaş M., Et M. 2013. On Pointwise and Uniform Statistical Convergence of Order for Sequences of Functions. Fixed Point Theory and Applications, 2013 (33): 1-11.
  • [15] Et M., Tripathy B.C., Dutta A.J. 2014. On Pointwise Statistical Convergence of Order of Sequences of Fuzzy Mappings. Kuwait Journal of Science, 41 (3): 17-30.
  • [16] Et M., Çolak R., Altın Y. 2014. Strongly Almost Summable Sequences of Order . Kuwait Journal of Science, 41 (2): 35–47.
  • [17] Işık M., Akbaş K.E. 2017. On Statistical Convergence of order in Probability. Journal of Inequalities and Special Functions, 8 (4): 57–64.
  • [18] Mohiuddine S.A., Alotaibi A., Mursaleen M. 2013. Statistical Convergence Through De La Vallee-Poussin Mean in Locally Solid Riesz Spaces. Advances in Difference Equations, 2013 (66): 1-10.
  • [19] Mursaleen M. 2000. Statistical Convergence. Mathematica Slovaca, 50 (1): 111–115.
  • [20]Salat T. 1980. On Statistically Convergent Sequences of Real Numbers. Mathematica Slovaca, 30 (2): 139-150.
  • [21] Srivastava H.M., Et M. 2017. Lacunary Statistical Convergence and Strongly Lacunary Summable Functions of Order. Filomat, 31 (6): 1573–1582.
  • [22] Çolak R., Bektaş Ç.A. 2011. Statistical Convergence of Order . Acta Mathematica Scientia, 31 (3): 953-959.
  • [23]Gadjiev A.D., Orhan C. 2002. Some Approximation Theorems via Statistical Convergence. Rocky Mountain Journal of Mathematics, 32 (1): 129-138.
  • [24]Çolak R. 2010. Statistical Convergence of Order . Modern Methods in Analysis and Its Applications, Edited by Mursaleen M., Anamaya Publishers, New Delhi, India, 121-129.
  • [25]Başar F. 2011. Summability Theory and Its Applications. Bentham Science Publishers, İstanbul, 1-402.
  • [26]Wilansky A. 2000. Summability Through Functional Analysis. Elseiver Science Publishers, Amsterdam, 1-317.

Lucas Type Statistical Convergence of Order α

Year 2020, Volume: 9 Issue: 4, 1537 - 1544, 25.12.2020

Murat Karakaş Hacer Dönmez

Abstract

Fibonacci and Lucas numbers have become a part of approximation of introducing a sequence space by tha aid of matrix domain of an infinite matrix in the last decade. So, the main goal of the article is to establish a new regular matrix and new sequence space with the help of Lucas numbers. Also, we examine statistical convergence of order and its some properties by using Lucas sequence which is obtained from the terms of Lucas matrix. Also, we give some topological properties and inclusion relations about these two concepts.

Keywords

Lucas sequence Lucas numbers Statistical Convergence Sequence space

References

  • [1] Vajda S. 1989. Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications. Dover Publications Inc., New York, 1-190.
  • [2] Kalman D., Mena R. 2003. The Fibonacci Numbers: Exposed. Mathematics Magazine, 76 (3): 167-181.
  • [3] Candan M., Kara E.E. 2015. A Study on Topological and Geometrical Characteristics of new Banach Sequence Spaces. Gulf Journal of Mathematics, 3 (4): 67-84.
  • [4] Kılınç G., Candan M. 2017. Some Generalized Fibonacci Difference Spaces Defined by a Sequence of Modulus Functions. Facta Universitatis, Series: Mathematics and Informatics, 32 (1): 95-116.
  • [5] Kara E.E. 2013. Some Topological and Geometrical Properties of New Banach Sequence Spaces. Journal of Inequalities and Applications, 2013 (38): 1-15.
  • [6] Kara E.E., Başarır M. 2012. An Application of Fibonacci Numbers into Infinite Toeplitz Matrices. Caspian Journal of Mathematics Sciences, 1 (1): 1-6.
  • [7] Karakaş M. 2015. A New Regular Matrix Defined by Fibonacci Numbers and Its Applications. BEU Journal of Science, 4 (2): 205-210.
  • [8] Karakaş M., Karakaş A.M. 2018. A Study on Lucas Difference Sequence Spaces and . Maejo International Journal of Science and Technology, 12 (1): 70-78.
  • [9] Karakaş M., Akbaş T., Karakaş A.M. 2019. On the Lucas Difference Sequence Spaces Defined by Modulus Function. Applications and Applied Mathematics, 14 (1): 235-244.
  • [10] Fast H. 1951. Sur La Convergence Statistique. Colloquium Mathematicum, 2: 241-244.
  • [11] Steinhaus H. 1951. Sur la Convergence Ordinaire et La Convergence Asymptotique. Colloquium Mathematicum, 2: 73–74.
  • [12] Fridy J.A. 1985. On Statistical Convergence. Analysis, 5: 301–313.
  • [13] Connor J.S. 1988. The Statistical and Strong p-Cesàro Convergence of Sequences. Analysis, 8: 47–63.
  • [14] Çınar M., Karakaş M., Et M. 2013. On Pointwise and Uniform Statistical Convergence of Order for Sequences of Functions. Fixed Point Theory and Applications, 2013 (33): 1-11.
  • [15] Et M., Tripathy B.C., Dutta A.J. 2014. On Pointwise Statistical Convergence of Order of Sequences of Fuzzy Mappings. Kuwait Journal of Science, 41 (3): 17-30.
  • [16] Et M., Çolak R., Altın Y. 2014. Strongly Almost Summable Sequences of Order . Kuwait Journal of Science, 41 (2): 35–47.
  • [17] Işık M., Akbaş K.E. 2017. On Statistical Convergence of order in Probability. Journal of Inequalities and Special Functions, 8 (4): 57–64.
  • [18] Mohiuddine S.A., Alotaibi A., Mursaleen M. 2013. Statistical Convergence Through De La Vallee-Poussin Mean in Locally Solid Riesz Spaces. Advances in Difference Equations, 2013 (66): 1-10.
  • [19] Mursaleen M. 2000. Statistical Convergence. Mathematica Slovaca, 50 (1): 111–115.
  • [20]Salat T. 1980. On Statistically Convergent Sequences of Real Numbers. Mathematica Slovaca, 30 (2): 139-150.
  • [21] Srivastava H.M., Et M. 2017. Lacunary Statistical Convergence and Strongly Lacunary Summable Functions of Order. Filomat, 31 (6): 1573–1582.
  • [22] Çolak R., Bektaş Ç.A. 2011. Statistical Convergence of Order . Acta Mathematica Scientia, 31 (3): 953-959.
  • [23]Gadjiev A.D., Orhan C. 2002. Some Approximation Theorems via Statistical Convergence. Rocky Mountain Journal of Mathematics, 32 (1): 129-138.
  • [24]Çolak R. 2010. Statistical Convergence of Order . Modern Methods in Analysis and Its Applications, Edited by Mursaleen M., Anamaya Publishers, New Delhi, India, 121-129.
  • [25]Başar F. 2011. Summability Theory and Its Applications. Bentham Science Publishers, İstanbul, 1-402.
  • [26]Wilansky A. 2000. Summability Through Functional Analysis. Elseiver Science Publishers, Amsterdam, 1-317.
There are 26 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Murat Karakaş 0000-0002-5174-0282

Hacer Dönmez This is me 0000-0002-1043-510X

Publication Date December 25, 2020
Submission Date July 21, 2020
Acceptance Date October 3, 2020
Published in Issue Year 2020 Volume: 9 Issue: 4

Cite

IEEE M. Karakaş and H. Dönmez, “Lucas Type Statistical Convergence of Order α”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 4, pp. 1537–1544, 2020.
 Download Cover Image

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS