Küme Dizilerinin Modülüs Foksiyonu Yardımıyla Tanımlanan Asimptotik 𝓘-İnvaryant İstatistiksel Denkliği
Yıl 2018,
Cilt: 18 Sayı: 2, 477 - 485, 31.08.2018
Nimet P. Akın
,
Erdinç Dündar
Öz
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.
Kaynakça
- 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.
Yıl 2018,
Cilt: 18 Sayı: 2, 477 - 485, 31.08.2018
Nimet P. Akın
,
Erdinç Dündar
Kaynakça
- 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.