On $\rho -$Statistical Convergence of Interval Numbers

Year 2026, Volume: 14 Issue: 1 , 181 - 184 , 30.04.2026

Hafize Gumus , Hasan Hüseyin Güleç

https://izlik.org/JA83KZ65LS

Abstract

With the definition of interval numbers in 1951, studies such as comparing these numbers and examining the arithmetic operations that can be performed with these numbers have attracted considerable interest. These studies continued with studies investigating the properties of interval number sequence spaces and whether interval number sequences satisfy convergence conditions such as classical convergence and statistical convergence. At the same time, it is quite common to examine the concept of statistical convergence from different perspectives using different sequences. In this context, we investigate $\rho -$statistical convergence of interval numbers, we give our main definitions and prove some inclusion theorems in this paper.

Keywords

interval numbers. , Statistical Convergence , ρ-statistical convergence

References

• [1] G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press , New York , 1983.
• [2] K. P. Chiao, Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematical Sciences, 18(2) (2002), 219-233.
• [3] H. C¸ akallı, A variation on statistical ward continuity, Bull. Malays. Math. Sci. Soc. 40 (2017), 1701-1710.
• [4] P. S. Dwyer, Linear Computation, New York, Wiley, 1951.
• [5] P. Erd¨os and G. Tenenbaum, Sur les densit´es de certaines suites d’entiers, Proceedings of the London Mathematical Society, 59(3) (1989), 417-438.
• [6] A. Esi, N. L. Braha and A. Rushiti, Wijsman l􀀀statistical convergence of interval numbers, Bol. Soc. Paran. Math., 35(2) (2017), 9-18.
• [7] A. Esi, Statistical and lacunary statistical convergence of intervalval numbers in topological groups, Acta Scientiarum Technology, 36(3) (2014), 491-495. doi: 10.4025/actascitechnol.v36i3.16545.
• [8] H. Fast, Sur la convergence statistique, Colloquium Mathematicae 2, (1951), 241-244 .
• [9] A. R. Freedman and J. J. Sember, Densities and summability, Pacific Journal of Mathematics, 95(2) (1981), 293-305.
• [10] J. A. Fridy, On statistical convergence, Analysis 5, 1985, 301-313.
• [11] K. Ganesan and P. Veeramani, On arithmetic operations of interval numbers, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(6) (2005), 619-631. https://doi.org/10.1142/S0218488505003710
• [12] H. S¸ . Kandemir, On r􀀀statistical convergence in topological groups, Maltepe Journal of Mathematics, 4(1) (2022), 9-14. https://doi.org/ 10.47087/mjm.1092559
• [13] H. I. Miller, A measure theoretical subsequence characterization of statistical convergence, Transactions of the American Mathematical Society, 347 (1995), 1811-1819.
• [14] R. E. Moore, Automatic Error Analysis in Digital Computation, LSMD-48421, Lockheed Missiles and Space Company, 1959.
• [15] R. E. Moore and C. T. Yang, Theory of an Interval Algebra and Its Application to Numeric Analysis, RAAG Memoris II, Gaukutsu Bunken Fukeyu-kai, Tokyo, 1958.
• [16] R. E. Moore and C. T. Yang, Interval Analysis I, LMSD-285875, Lockheed Missiles and Space Company, Palo Alto, Calif., 1959.
• [17] F. Nuray, U. Ulusu and E. D¨undar, Some properties of two dimensional interval numbers, Mathematical Sciences and Applications E-Notes, 10(2) ( 2022), 93-101.
• [18] I. J. Schoenberg, The integrability of certain functions and related summability methods, The American Mathematical Monthly 66 (1959), 361-375.
• [19] A. Sengupta and T. K. Pal, On comparing interval numbers, European Journal of Operational Research, 127(1) (2000), 28-43. https://doi.org/10.1016/S0377-2217(99)00319-7
• [20] H. Steinhaus, Sur la convergence ordiniaire et la convergence asymptotique, Colloquium Mathematicum 2, 1951, 73-84.
• [21] M. S¸eng¨on¨ul and A. Eryılmaz, On the sequence spaces of interval numbers, Thai Journal of Mathematics, 8(3) (2010), 503-510.
• [22] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.