In this paper, we give some basic properties in order to use statistical epi-convergence more efficiently in future studies. Such situations are studied: Uniform statistical convergence of sequence of functions, statistical epi-limit of compound of sequence of functions, statistical epi-limit of the sum of sequence of functions, the property of epi-limit function if the sequence of functions are lower semi-continuous and the convexity of epi-limit function if each function in the sequence is convex.
Anastassiou, A. G. and Duman, O., 2011. Towards Intelligent Modeling: Statistical Approximation Theory, vol.14, Berlin.
Attouch, H., 1977. Convergence de fonctions convexes, de sous-differentiels et semi-groupes. Comptes Rendus de lAcademie des Sciences de Paris, 284, 539-542.
Caserta, A. and Koc ̆inac, Lj. D. R., 2012. On statistical exhaustiveness. Applied Mathematics Letters, 25, 1447-1451.
Di Maio, G. and Koc ̆inac, Lj. D. R., 2008. Statistical convergence in topology. Topology and its Applications, 156, 28-45.
Duman, O. and Orhan, C., 2004. μ -statistically convergent function sequences. Czechoslovak Mathematical Journal, 54 (129)(2), 413-422.
Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241–244.
Fridy, J. A., 1993. Statistical limit points. Proceedings of the American Mathematical Society, 118 (4), 1182–1192.
Fridy, J. A. and Orhan, C., 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society, 125, 3625–3631.
Gökhan, A. and Güngör, M., 2002. On pointwise statistical convergence. Indian Journal of Pure and Applied Mathematics, 33 (9), 1379-1384.
Güngör, M. and Gökhan, A., 2005. On uniform statistical convergence. International Journal of Pure and Applied Mathematics, 19 (1), 17–24.
Joly, J.-L., 1973. Une famille de topologies sur lensemble des fonctions convexes pour lesquelles la polarite est bicontinue. Journal de Mathematiques Pures et Appliquees, 52, 421–441.
Maso, G. D., 1993. An introduction to Γ-convergence, vol.8, Boston.
McLinden, L. and Bergstrom, R., 1981. Preservation of convergence of sets and functions in finite dimensions. Transactions of the American Mathematical Society, 268, 127–142.
Mosco, U., 1969. Convergence of convex sets and of solutions of variational inequalities. Advances in Mathematics, 3, 510–585.
Niven, I. and Zuckerman, H. S., 1980. An Introduction to the Theory of Numbers, New York.
Rockafellar, R.T. and Wets, R.J-B., 2009. Variational Analysis, Berlin.
S ̆ala't, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150.
Salinetti, G. and Wets, R.J-B., 1977. On the relation between two types of convergence for convex functions. Journal of Mathematical Analysis and Applications, 60, 211–226.
Schoenberg, I.J.:, 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66, 361-375.
Steinhaus, H., 1951. Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum, 2, 73-74.
Talo, Ö., Sever, Y. and Başar, F., 2016. On statistically convergent sequences of closed sets. Filomat, 30 (6), 1497-1509.
Wets, R.J-B., 1980. Convergence of convex functions, variational inequalities and convex optimization problems, New York.
Wijsman, R. A., 1964. Convergence of sequences of convex sets, cones and functions. Bulletin of 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, 32-45.
Zygmund, A., 1979. Trigonometric Series, Cambridge University Press, Cambridge, UK.
İstatistiksel Epi-Yakınsaklık ile İlgili Temel Özellikler
Year 2020,
Volume: 20 Issue: 6, 968 - 974, 31.12.2020
Bu çalışmada, istatistiksel epi-yakınsaklığın sonraki çalışmalarda daha verimli kullanılabilmesi için bazı temel özelliklere yer verildi. Bir fonksiyon dizisinin düzgün istatistiksel yakınsaklık durumu, fonksiyon dizilerinin bileşkesinin istatistiksel epi-limiti, fonksiyon dizilerinin toplamının istatistiksel epi-limiti, fonksiyon dizisinin alttan yarı sürekli olması halinde epi-limit fonksiyonunun özelliği ve fonksiyon dizisindeki her bir fonksiyonun konveks olması halinde epi-limit fonksiyonunun konveksliği gibi durumlar çalışıldı.
Anastassiou, A. G. and Duman, O., 2011. Towards Intelligent Modeling: Statistical Approximation Theory, vol.14, Berlin.
Attouch, H., 1977. Convergence de fonctions convexes, de sous-differentiels et semi-groupes. Comptes Rendus de lAcademie des Sciences de Paris, 284, 539-542.
Caserta, A. and Koc ̆inac, Lj. D. R., 2012. On statistical exhaustiveness. Applied Mathematics Letters, 25, 1447-1451.
Di Maio, G. and Koc ̆inac, Lj. D. R., 2008. Statistical convergence in topology. Topology and its Applications, 156, 28-45.
Duman, O. and Orhan, C., 2004. μ -statistically convergent function sequences. Czechoslovak Mathematical Journal, 54 (129)(2), 413-422.
Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241–244.
Fridy, J. A., 1993. Statistical limit points. Proceedings of the American Mathematical Society, 118 (4), 1182–1192.
Fridy, J. A. and Orhan, C., 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society, 125, 3625–3631.
Gökhan, A. and Güngör, M., 2002. On pointwise statistical convergence. Indian Journal of Pure and Applied Mathematics, 33 (9), 1379-1384.
Güngör, M. and Gökhan, A., 2005. On uniform statistical convergence. International Journal of Pure and Applied Mathematics, 19 (1), 17–24.
Joly, J.-L., 1973. Une famille de topologies sur lensemble des fonctions convexes pour lesquelles la polarite est bicontinue. Journal de Mathematiques Pures et Appliquees, 52, 421–441.
Maso, G. D., 1993. An introduction to Γ-convergence, vol.8, Boston.
McLinden, L. and Bergstrom, R., 1981. Preservation of convergence of sets and functions in finite dimensions. Transactions of the American Mathematical Society, 268, 127–142.
Mosco, U., 1969. Convergence of convex sets and of solutions of variational inequalities. Advances in Mathematics, 3, 510–585.
Niven, I. and Zuckerman, H. S., 1980. An Introduction to the Theory of Numbers, New York.
Rockafellar, R.T. and Wets, R.J-B., 2009. Variational Analysis, Berlin.
S ̆ala't, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150.
Salinetti, G. and Wets, R.J-B., 1977. On the relation between two types of convergence for convex functions. Journal of Mathematical Analysis and Applications, 60, 211–226.
Schoenberg, I.J.:, 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66, 361-375.
Steinhaus, H., 1951. Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicum, 2, 73-74.
Talo, Ö., Sever, Y. and Başar, F., 2016. On statistically convergent sequences of closed sets. Filomat, 30 (6), 1497-1509.
Wets, R.J-B., 1980. Convergence of convex functions, variational inequalities and convex optimization problems, New York.
Wijsman, R. A., 1964. Convergence of sequences of convex sets, cones and functions. Bulletin of 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, 32-45.
Zygmund, A., 1979. Trigonometric Series, Cambridge University Press, Cambridge, UK.
Tortop, Ş. (2020). Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20(6), 968-974. https://doi.org/10.35414/akufemubid.819410
AMA
Tortop Ş. Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2020;20(6):968-974. doi:10.35414/akufemubid.819410
Chicago
Tortop, Şükrü. “Basic Properties of Statistical Epi-Convergence”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20, no. 6 (December 2020): 968-74. https://doi.org/10.35414/akufemubid.819410.
EndNote
Tortop Ş (December 1, 2020) Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 6 968–974.
IEEE
Ş. Tortop, “Basic Properties of Statistical Epi-Convergence”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 6, pp. 968–974, 2020, doi: 10.35414/akufemubid.819410.
ISNAD
Tortop, Şükrü. “Basic Properties of Statistical Epi-Convergence”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20/6 (December 2020), 968-974. https://doi.org/10.35414/akufemubid.819410.
JAMA
Tortop Ş. Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20:968–974.
MLA
Tortop, Şükrü. “Basic Properties of Statistical Epi-Convergence”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 6, 2020, pp. 968-74, doi:10.35414/akufemubid.819410.
Vancouver
Tortop Ş. Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20(6):968-74.