ASYMPTOTICALLY I-STATISTICAL EQUIVALENT FUNCTIONS DEFINED ON AMENABLE SEMIGROUPS

Year 2019, Volume: 37 Issue: 4, 1366 - 1373, 01.12.2019

Uğur Ulusu Erdinç Dündar Bünyamin Aydın

Abstract

In this study, we introduce the notions of asymptotically I-equivalence, asymptotically I^*-equivalence, asymptotically strongly I-equivalence and asymptotically I-statistical equivalence for functions defined on discrete countable amenable semigroups. Also, we examine some properties of these notions and relationships between them.

Keywords

Statistical convergence , ideal convergence , asymptotically equivalence , folner sequence , amenable semigroups.

References

• [1] Fast H., (1951) Sur la convergence statistique, Colloq. Math. 2, 241–244.
• [2] Connor J.S., (1988) The statistical and strong p-Cesaro convergence of sequences, Analysis 8, 46–63.
• [3] Fridy J.A., (1985) On statistical convergence, Analysis 5, 301–313.
• [4] Šalát T., (1980) On statistically convergent sequences of real numbers, Math. Slovaca 30(2), 139–150.
• [5] Kostyrko P., Šalát T. and Wilczyński W., (2000) I-Convergence, Real Anal. Exchange 26(2), 669–686.
• [6] Das P., Savaş E. and Ghosal S.Kr., (2011) On generalizations of certain summability methods using ideals, Appl. Math. Letters 24, 1509–1514.
• [7] Day M., (1957) Amenable semigroups, Illinois J. Math. 1, 509–544.
• [8] Douglass S.A., (1968) On a concept of summability in amenable semigroups, Math. Scand. 28, 96–102.
• [9] Douglass S.A., (1973) Summing sequences for amenable semigroups, Michigan Math. J. 20, 169–179.
• [10] Mah P.F., (1971) Summability in amenable semigroups, Trans. Amer. Math. Soc. 156, 391–403.
• [11] Mah P.F., (1972) Matrix summability in amenable semigroups, Proc. Amer. Math. Soc. 36, 414–420.
• [12] Nuray F. and Rhoades B.E., (2011) Some kinds of convergence defined by Folner sequences, Analysis 31(4), 381–390.
• [13] Ulusu U., Dündar E. and Nuray F., (2019) Some generalized convergence types using ideals in amenable semigroups, Bull. Math. Anal. Appl. 11(1), 28-35.
• [14] Marouf M., (1993) Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4), 755–762.
• [15] Hazarika B., (2015) On asymptotically ideal equivalent sequences, Journal of the Egyptian Mathematical Society 23(1), 67-72.
• [16] Patterson R.F., (2003) On asymptotically statistically equivalent sequences, Demostratio Mathematica 36(1), 149-153.
• [17] Savaş E., (2013) On I-asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ. 111, 7 pages. doi:10.1186/1687-1847-2013-111.
• [18] Nuray F. and Rhoades B.E., (2013) Asymptotically and statistically equivalent functions defined on amenable semigroups, Thai J. Math. 11(2), 303–311.
• [19] Namioka I., (1964) Følner’s conditions for amenable semigroups, Math. Scand. 15, 18–28.