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.