On the K_{a}-continuity of real functions

Year 2020, Volume: 69 Issue: 1, 540 - 546, 30.06.2020

Sevda Yıldız , Kamil Demirci , Fadime Dirik

https://doi.org/10.31801/cfsuasmas.569892

Abstract

The aim of the present paper is to define K_{a}-continuity which is associated to the number sequence a=(a_{n}) and to give some new results.

Keywords

K_a-continuity, F-continuity, A-continuity

References

• Aczel, J., Vorlesungen über Funktionalgleichungen und ihre Anwendungen, VEB Deutsch. Verlag der Wissenschaften, Berlin, 1961.
• Antoni, J., On the A-continuity of real functions II, Math. Slovaca 36 (1986), 283-288.
• Antoni, J., Salat, T., On the A-continuity of real functions, Acta Math. Univ. Comenian. 39 (1980), 159-164.
• Borsik, J., Salat, T., On F-continuity of real functions, Tatra Mountains Math. Publ., 2 (1993), 37-42.
• Boos, J., Classical and modern in summability, Oxford Science Publications, 2000.
• Hardy, G. H., Divergent series, Oxford Univ. Press, London, 1949.
• Lazic, M., Jovovic, V., Cauchy's operators and convergence methods, Univ. Beograd. Publ. Elektrothen Fak. 4 (1993), 81-87.
• Lorentz, G. G., A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190.
• Robbins, H., Problem 4216, Amer. Math. Monthly, 53 (1946), 470-471.
• Problem 4216 (1946, 470) Amer. Math. Monthly, Propesed H. Robins. Solution by R. c. Buck, Amer. Math. Monthly 55 (1948) 36.
• Öztürk, E., On almost continuity and almost A-continuity of real functions, Comm. Fac. Sci. Univ. Ankara, Ser. A, 32 (1983), 25-30.
• Posner, E. C., Summability preserving functions, Proc. Amer. Math. Soc., 12 (1961), 73-76.
• Savaş, E., Das, G., On the A-continuity of real functions, istanbul Üniv. Fen. Fak. Mat. Der., 53 (1994), 61-66.