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Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği

Year 2018, Volume: 18 Issue: 2, 477 - 485, 31.08.2018

Nimet P. Akın , Erdinç Dündar

Abstract

Bu çalışmada küme dizileri için kuvvetli asimptotik ℐ-invaryant denklik, 𝑓-asimptotik ℐ-invaryant denklik, kuvvetli 𝑓-asimptotik ℐ-invaryant denklik ve asimptotik ℐ-invaryant istatistiksel denklik tanımları verildi. Daha sonra, verilen bu yeni kavramlar arasındaki ilişkiler incelendi.

Keywords

Asimptotik denklik Modülüs fonsiyonu ℐ-yakınsaklık ℐ-İnvaryant denklik.

References

  • Baronti M., and Papini P., 1986. Convergence of sequences of sets, In: Methods of functional analysis in approximation theory (pp. 133-155), ISNM 76, Birkhäuser, Basel. Beer G., 1985. On convergence of closed sets in a metric space and distance functions. Bulletin of the Australian Mathematical Society, 31, 421-432.
  • Beer G., 1994. Wijsman convergence: A survey. Set-Valued Analysis, 2 , 77-94.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
  • Kara E. E., Daştan M., İlkhan M., 2016. On almost ideal convergence with respect to an Orlicz function. Konuralp Journal of Mathematics, 4(2), 87-94.
  • Kara E. E., Daştan M., İlkhan M., 2017. On Lacunary ideal convergence of some sequences. New Trends in Mathematical Sciences, 5(1), 234-242.
  • Kişi, Ö. and Nuray, F., 2013. A new convergence for sequences of sets. Abstract and Applied Analysis, Article ID 852796.
  • Kişi Ö., Gümüş H. and Nuray F., 2015. ℐ-Asymptotically lacunary equivalent set sequences defined by modulus function. Acta Universitatis Apulensis, 41, 141-151.
  • Kostyrko P., Šalát T. and Wilczyński W., 2000. ℐ-Convergence. Real Analysis Exchange, 26(2), 669-686.
  • Kumar V. and Sharma A., 2012. Asymptotically lacunary equivalent sequences defined by ideals and modulus function. Mathematical Sciences, 6(23), 5 pages. Lorentz G., 1948. A contribution to the theory of divergent sequences. Acta Mathematica, 80, 167-190.
  • Maddox J., 1986. Sequence spaces defined by a modulus. Mathematical Proceedings of the Cambridge Philosophical Society, 100, 161-166.
  • Marouf, M., 1993. Asymptotic equivalence and summability. International Journal of Mathematics and Mathematical Sciences, 16(4), 755-762.
  • Mursaleen, M. and Edely, O. H. H., 2009. On the invariant mean and statistical convergence. Applied Mathematics Letters, 22(11), 1700-1704.
  • Mursaleen, M., 1983. Matrix transformation between some new sequence spaces. Houston Journal of Mathematics, 9, 505-509.
  • Mursaleen, M., 1979. On finite matrices and invariant means. Indian Journal of Pure and Applied Mathematics, 10, 457-460.
  • Nakano H., 1953. Concave modulars. Journal of the Mathematical Society Japan, 5 ,29-49.
  • Nuray F. and Rhoades B. E., 2012. Statistical convergence of sequences of sets. Fasiciculi Mathematici, 49 , 87-99.
  • Nuray, F. and Savaş, E., 1994. Invariant statistical convergence and 𝐴-invariant statistical convergence. Indian Journal of Pure and Applied Mathematics, 25(3), 267-274.
  • Nuray, F., Gök, H. and Ulusu, U., 2011. ℐ𝜎-convergence. Mathematical Communications, 16, 531-538.
  • Pancaroğlu, N. and Nuray, F., 2013a. Statistical lacunary invariant summability. Theoretical Mathematics and Applications, 3(2), 71-78.
  • Pancaroğlu N. and Nuray F., 2013b. On Invariant Statistically Convergence and Lacunary Invariant Statistically Convergence of Sequences of Sets. Progress in Applied Mathematics, 5(2), 23-29.
  • Pancaroğlu N. and Nuray F. and Savaş E., 2013. On asymptotically lacunary invariant statistical equivalent set sequences. AIP Conf. Proc. 1558(780) http://dx.doi.org/10.1063/1.4825609
  • Pancaroğlu N. and Nuray F., 2014. Invariant Sta- tistical Convergence of Sequences of Sets with respect to a Modulus Function. Abstract and Applied Analysis, Article ID 818020, 5 pages.
  • Patterson, R. F., 2003. On asymptotically statistically equivalent sequences. Demostratio Mathematica, 36(1), 149-153.
  • Pehlivan S., and Fisher B., 1995. Some sequences spaces defined by a modulus. Mathematica Slovaca, 45, 275-280.
  • Raimi, R. A., 1963. Invariant means and invariant matrix methods of summability. Duke Mathematical Journal, 30(1), 81-94.
  • Savaş, E., 1989a. Some sequence spaces involving invariant means. Indian Journal of Mathematics, 31, 1-8.
  • Savaş, E., 1989b. Strongly 𝜎-convergent sequences. Bulletin of Calcutta Mathematical Society, 81, 295-300.
  • Savaş, E., 2013. On ℐ-asymptotically lacunary statistical equivalent sequences. Advances inDifference Equations, 111(2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • Savaş, E. and Nuray, F., 1993. On 𝜎-statistically convergence and lacunary 𝜎-statistically convergence. Mathematica Slovaca, 43(3), 309-315.
  • Schaefer, P., 1972. Infinite matrices and invariant means. Proceedings of the American Mathe-matical Society, 36, 104-110.
  • Schoenberg I. J., 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66, 361-375.
  • Ulusu U. and Nuray F., 2013. On asymptotically lacunary statistical equivalent set sequences. Journal of Mathematics, Article ID 310438, 5 pages.
  • Ulusu U. and Gülle E., Asymptotically ℐσ-equiva-lence of sequences of sets. (yayın aşamasında).
  • Ulusu U. and Dündar E., 2018. Asymptotically ℐ- Ces`aro Equivalence of Sequences of Sets. Universal Journal of Mathematics and Applications, 1(2), 101-105.
  • Wijsman R. A., 1964. Convergence of sequences of convex sets, cones and functions. Bulletin American Mathematical Society, 70, 186-188.
  • Wijsman R. A., 1966. Convergence of Sequences of Convex sets, Cones and Functions II. Transactions of the American Mathematical Society, 123(1) , 32-45.

Year 2018, Volume: 18 Issue: 2, 477 - 485, 31.08.2018

Nimet P. Akın , Erdinç Dündar

Abstract

References

  • Baronti M., and Papini P., 1986. Convergence of sequences of sets, In: Methods of functional analysis in approximation theory (pp. 133-155), ISNM 76, Birkhäuser, Basel. Beer G., 1985. On convergence of closed sets in a metric space and distance functions. Bulletin of the Australian Mathematical Society, 31, 421-432.
  • Beer G., 1994. Wijsman convergence: A survey. Set-Valued Analysis, 2 , 77-94.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
  • Kara E. E., Daştan M., İlkhan M., 2016. On almost ideal convergence with respect to an Orlicz function. Konuralp Journal of Mathematics, 4(2), 87-94.
  • Kara E. E., Daştan M., İlkhan M., 2017. On Lacunary ideal convergence of some sequences. New Trends in Mathematical Sciences, 5(1), 234-242.
  • Kişi, Ö. and Nuray, F., 2013. A new convergence for sequences of sets. Abstract and Applied Analysis, Article ID 852796.
  • Kişi Ö., Gümüş H. and Nuray F., 2015. ℐ-Asymptotically lacunary equivalent set sequences defined by modulus function. Acta Universitatis Apulensis, 41, 141-151.
  • Kostyrko P., Šalát T. and Wilczyński W., 2000. ℐ-Convergence. Real Analysis Exchange, 26(2), 669-686.
  • Kumar V. and Sharma A., 2012. Asymptotically lacunary equivalent sequences defined by ideals and modulus function. Mathematical Sciences, 6(23), 5 pages. Lorentz G., 1948. A contribution to the theory of divergent sequences. Acta Mathematica, 80, 167-190.
  • Maddox J., 1986. Sequence spaces defined by a modulus. Mathematical Proceedings of the Cambridge Philosophical Society, 100, 161-166.
  • Marouf, M., 1993. Asymptotic equivalence and summability. International Journal of Mathematics and Mathematical Sciences, 16(4), 755-762.
  • Mursaleen, M. and Edely, O. H. H., 2009. On the invariant mean and statistical convergence. Applied Mathematics Letters, 22(11), 1700-1704.
  • Mursaleen, M., 1983. Matrix transformation between some new sequence spaces. Houston Journal of Mathematics, 9, 505-509.
  • Mursaleen, M., 1979. On finite matrices and invariant means. Indian Journal of Pure and Applied Mathematics, 10, 457-460.
  • Nakano H., 1953. Concave modulars. Journal of the Mathematical Society Japan, 5 ,29-49.
  • Nuray F. and Rhoades B. E., 2012. Statistical convergence of sequences of sets. Fasiciculi Mathematici, 49 , 87-99.
  • Nuray, F. and Savaş, E., 1994. Invariant statistical convergence and 𝐴-invariant statistical convergence. Indian Journal of Pure and Applied Mathematics, 25(3), 267-274.
  • Nuray, F., Gök, H. and Ulusu, U., 2011. ℐ𝜎-convergence. Mathematical Communications, 16, 531-538.
  • Pancaroğlu, N. and Nuray, F., 2013a. Statistical lacunary invariant summability. Theoretical Mathematics and Applications, 3(2), 71-78.
  • Pancaroğlu N. and Nuray F., 2013b. On Invariant Statistically Convergence and Lacunary Invariant Statistically Convergence of Sequences of Sets. Progress in Applied Mathematics, 5(2), 23-29.
  • Pancaroğlu N. and Nuray F. and Savaş E., 2013. On asymptotically lacunary invariant statistical equivalent set sequences. AIP Conf. Proc. 1558(780) http://dx.doi.org/10.1063/1.4825609
  • Pancaroğlu N. and Nuray F., 2014. Invariant Sta- tistical Convergence of Sequences of Sets with respect to a Modulus Function. Abstract and Applied Analysis, Article ID 818020, 5 pages.
  • Patterson, R. F., 2003. On asymptotically statistically equivalent sequences. Demostratio Mathematica, 36(1), 149-153.
  • Pehlivan S., and Fisher B., 1995. Some sequences spaces defined by a modulus. Mathematica Slovaca, 45, 275-280.
  • Raimi, R. A., 1963. Invariant means and invariant matrix methods of summability. Duke Mathematical Journal, 30(1), 81-94.
  • Savaş, E., 1989a. Some sequence spaces involving invariant means. Indian Journal of Mathematics, 31, 1-8.
  • Savaş, E., 1989b. Strongly 𝜎-convergent sequences. Bulletin of Calcutta Mathematical Society, 81, 295-300.
  • Savaş, E., 2013. On ℐ-asymptotically lacunary statistical equivalent sequences. Advances inDifference Equations, 111(2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • Savaş, E. and Nuray, F., 1993. On 𝜎-statistically convergence and lacunary 𝜎-statistically convergence. Mathematica Slovaca, 43(3), 309-315.
  • Schaefer, P., 1972. Infinite matrices and invariant means. Proceedings of the American Mathe-matical Society, 36, 104-110.
  • Schoenberg I. J., 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66, 361-375.
  • Ulusu U. and Nuray F., 2013. On asymptotically lacunary statistical equivalent set sequences. Journal of Mathematics, Article ID 310438, 5 pages.
  • Ulusu U. and Gülle E., Asymptotically ℐσ-equiva-lence of sequences of sets. (yayın aşamasında).
  • Ulusu U. and Dündar E., 2018. Asymptotically ℐ- Ces`aro Equivalence of Sequences of Sets. Universal Journal of Mathematics and Applications, 1(2), 101-105.
  • Wijsman R. A., 1964. Convergence of sequences of convex sets, cones and functions. Bulletin American Mathematical Society, 70, 186-188.
  • Wijsman R. A., 1966. Convergence of Sequences of Convex sets, Cones and Functions II. Transactions of the American Mathematical Society, 123(1) , 32-45.
There are 36 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Nimet P. Akın

Erdinç Dündar

Publication Date August 31, 2018
Submission Date January 12, 2018
Published in Issue Year 2018 Volume: 18 Issue: 2

Cite

APA Akın, N. P., & Dündar, E. (2018). Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 18(2), 477-485.
AMA Akın NP, Dündar E. Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. August 2018;18(2):477-485.
Chicago Akın, Nimet P., and Erdinç Dündar. “Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18, no. 2 (August 2018): 477-85.
EndNote Akın NP, Dündar E (August 1, 2018) Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18 2 477–485.
IEEE N. P. Akın and E. Dündar, “Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 2, pp. 477–485, 2018.
ISNAD Akın, Nimet P. - Dündar, Erdinç. “Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18/2 (August 2018), 477-485.
JAMA Akın NP, Dündar E. Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18:477–485.
MLA Akın, Nimet P. and Erdinç Dündar. “Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 2, 2018, pp. 477-85.
Vancouver Akın NP, Dündar E. Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18(2):477-85.