Statistical extension some types of symmetrically continuity

Pelda  Evirgen; Mehmet Kucukaslan

doi:10.26637/mjm1102/007

Abstract

In this paper, the notions symmetric continuity, weak continuity, weak symmetric continuity which was
introduced in [P.Pongsriiam and T.Thongsiri, Weakly symmetrically continuous function, Chamchuri Journal of Mathematics, vol 8(2016),49-65 ] are generalized by using natural density defined on N. Among the others some basic properties of generalized form of symmetrically continuity is investigate with several useful examples.

Keywords:

Continuity , symmetric continuity, statistical strong weak symmetric continuity, statistical weak continuity, statistical weak symmetric continuity

Mathematics Subject Classification:

General Mathematics

Authors Imprint References Funding Related Articles Downloads

Pelda Evirgen Institute of Science, Department of Mathematics, Mersin University, Mersin, Turkey. https://orcid.org/0000-0002-1295-339X
Mehmet Kucukaslan Faculty of Science, Department of Mathematics, Mersin University, Mersin, Turkey. https://orcid.org/0000-0002-3183-3123

Pages: 181-199
Date Published: 01-04-2023
Vol. 11 No. 02 (2023): Malaya Journal of Matematik (MJM)

M. A LTINOK , U. K AYA AND M. K¨ UCUKASLAN , Statistical extension of bounded sequence space, Commun.Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 70(1)(2021), 82-991, https://doi.org/10.31801/cfsuasmas.736132. DOI: https://doi.org/10.31801/cfsuasmas.736132

C. L. B ELNA , Symmetric continuity of real functions, Proc. American Math. Soc., 87(1983), 99-102, DOI: https://doi.org/10.1090/S0002-9939-1983-0677241-1

https://doi.org/10.2307/2044361. DOI: https://doi.org/10.2307/2044361

B. B ILALOV AND T. N AZAROVA , On statistical type convergence in uniform spaces, Bull. Iranian Math. Soc.,42(4)(2016), 975-986.

M. C HLEBIK , On symmetrically continuous functions, Real Anal. Exchange, 13(1987/88), 34,

https://doi.org/10.2307/44151838. DOI: https://doi.org/10.2307/44151838

J. C ERVENANSKY , Statistical convergence and statistical continuity, Sbornik Vedeckych Prac MtF STU,

(1998), 207-212.

J. C ONNOR AND K. G ROSSE -E RDMANN , Sequential Definitions of Continuity for Real Functions, Rocky

Mountain J. Math., 33(1)(2003), 93-120, https://doi.org/10.1216/rmjm/1181069988. DOI: https://doi.org/10.1216/rmjm/1181069988

M. E T AND H. S ENGUL , Some Cesaro type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8)(2014), 1593-1602, https://doi.org/10.2298/FIL1408593E. DOI: https://doi.org/10.2298/FIL1408593E

H. F AST , Sur la convergence statistique, Colloq. Math., 2(1951), 241-244, https://doi.org/10.4064/CM-2-3-4-241-244.

J. A. F RIDY , On statistical convergence, Analysis, 5(1985), 301-313, https://doi.org/10.1524/anly.1985.5.4.301. DOI: https://doi.org/10.1524/anly.1985.5.4.301

J. A. F RIDY AND C. O RHAN , Lacunary statistical convergence, Pasific. J. Math., 160(1993), 43-51,

https://doi.org/10.2140/pjm.1993.160.43. DOI: https://doi.org/10.2140/pjm.1993.160.43

H. F RIED , Uber die symmetrische Stetigkeit von Funktionen, Fund. Math., 29(1)(1937), 136-137. DOI: https://doi.org/10.4064/fm-29-1-136-137

E. H ALFER , Conditions implying continuity of functions, Proc. Amer. Math. Soc., 11(1960), 688-691,

https://doi.org/10.1090/S0002-9939-1960-0117699-4. DOI: https://doi.org/10.1090/S0002-9939-1960-0117699-4

J. J ASKULA AND B. S ZKOPI ´ NSKA , On the set of points of symmetric continuity, An. Univ. Bucures ¸ti Mat., 37(1988), 29-35.

M. K¨UCUKASLAN , U. D EGER AND O. D OVGOSHEY , Onthestatisticalconvergenceofmetric-valuedsequences, Ukrainian Math. J., 66(5)(2014), 712-720, https://doi.org/10.1007/s11253-014-0974-z. DOI: https://doi.org/10.1007/s11253-014-0974-z

S. M AZURKIEWICZ , On the relation between the existence of the second generalized derivative and the

continuity of a function (in Polish), Prace Matematyczno Fizyczne, 30(1919), 225-242.

H. I. M ILLER , A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(1995), 1811-1819, https://doi.org/10.1090/S0002-9947-1995-1260176-6. DOI: https://doi.org/10.1090/S0002-9947-1995-1260176-6

J. C. M ORAN AND V. L IENHARD , The statistical convergence of aerosol deposition measurements,

Experiments in Fluids, 22(1997), 375-379, https://doi.org/10.1007/s003480050063. DOI: https://doi.org/10.1007/s003480050063

A. N OWIK AND M. S ZYSZKOWSKI , Points of weak symmetry, Real Anal. Exchange, 32(2)(2007), 563–568,

https://doi.org/10.14321/realanalexch.32.2.0563. DOI: https://doi.org/10.14321/realanalexch.32.2.0563

D. O PPEGAARD , Generalizations of continuity, symmetry and symmetric continuity, Thesis, North Carol.

State Univ., (1993).

W. J. P ERVIN AND N. L EVINE , Connected mappings of Hausdorff spaces, Proc. Amer. Math. Soc., 9(1958), 488-496, https://doi.org/10.2307/2033013. DOI: https://doi.org/10.1090/S0002-9939-1958-0095468-2

P. P ONGSRIIAM , T. K HEMARATCHATAKUMTHORN , I. T ERMWUTTIPONG AND N. T RIPHOP , Some remarks on symmetric continuity of functions, Thai J. Math., Special Issue(2004), 31–36.

P. P ONGSRIIAM , T. K HEMARATCHATAKUMTHORN , I. T ERMWUTTIPONG AND N. T RIPHOP , On weak continuity of functions, Thai J. Math., 3(1)(2005), 7–16.

P. P ONGSRIIAM AND T. T HONGSIRI , Weakly symmetrically continuous function, Chamchuri J. Math.,

(2016), 49–65.

S. P. P ONOMAREV , Symmetrically continuous functions, Mat. Zametki., 1(1967), 385–390,

https://doi.org/10.1007/BF01095540. DOI: https://doi.org/10.1007/BF01095540

D. P REISS , A note on symmetrically continuous functions, Casopis Pest. Mat., 96(1971), 262-264,

https://doi.org/10.21136/CPM.1971.117723. DOI: https://doi.org/10.21136/CPM.1971.117723

T. S AL ´ AT , On statistically convergent sequences of real numbers, Math. Slovaca, 30(1980), 139-150.

I. J. S CHOENBERG , The integrability of certain functions and related summability methods, Amer. Math.

Monthly, 66(1959), 361-375, https://doi.org/10.2307/2308747. DOI: https://doi.org/10.2307/2308748

H. S TEINHAUS , Sur la Convergence Ordinaire et la Convergence Asymptotique, Colloq. Math., 2(1951), DOI: https://doi.org/10.4064/cm-2-3-4-241-244

-74.

M. S ZYSZKOWSKI , Points of weak symmetric continuity, Real Anal. Exchange, 24(2)(1998–1999), 807–813,

https://doi.org/10.2307/44152998. DOI: https://doi.org/10.2307/44152998

J. U HER , Symmetric continuity implies continuity, Trans. Amer. Math. Soc., 293(1986), 421-429, DOI: https://doi.org/10.1090/S0002-9947-1986-0814930-7

https://doi.org/10.2307/2000289. DOI: https://doi.org/10.2307/2000289