TY - JOUR T1 - On the Statistical Limits of Strongly Measurable Fuzzy Valued Functions AU - Yavuz, Enes AU - Talo, Özer AU - Çoşkun, Hüsamettin PY - 2020 DA - April Y2 - 2020 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 62 EP - 69 VL - 8 IS - 1 LA - en AB - We introduce the notions of statistical limit, statistical Cesaro summability of strongly measurable fuzzy valued functions and give slowly decreasing-slowly oscillating type Tauberian conditions under which statistical limits and statistical Cesaro summability of fuzzy valued functions imply ordinary limits in fuzzy number space. KW - fuzzy set theory KW - statistical limits KW - Ces\`{a}ro summability KW - Tauberian theorems CR - [1] S. Aytar, M. Mammadov and S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Set Syst 157, No. 7 (2006) 976–985. CR - [2] S. Aytar and S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Inform. Sci. 177, No. 16 (2007) 3290–3296 CR - [3] B. Bede and S. G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Set Syst 147, (2004) 385–403. CR - [4] C. Belen, Tauberian theorems for weighted mean summability method of improper Riemann integrals of fuzzy-number-valued functions, Soft Comput 22, No. 12 (2018) 3951–3957 CR - [5] C. Belen, Tauberian theorems for statistical limit and statistical summability by weighted means of continuous fuzzy valued functions, J. Math. Ext. (2020), preprint CR - [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2, (1951) 241–244. CR - [7] O. Kaleva, Fuzzy differential equations, Fuzzy Set Syst 24, (1987) 301–317. CR - [8] Y. K. Kim and B. M. Ghil, Integrals of fuzzy-number-valued functions, Fuzzy Set Syst 86, (1997) 213–222 CR - [9] H. Li and C. Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Set Syst 158, (2007) 2317–2338. CR - [10] J. Li, A. Zhao and J. Yan, The Cauchy problem of fuzzy differential equations under generalized differentiability, Fuzzy Set Syst 200, (2012) 1–24. CR - [11] F. Moricz, Statistical limits of measurable functions, Analysis 24, (2004) 1–18. CR - [12] F. Moricz, Statistical extensions of some classical Tauberian theorems in nondiscrete setting, Colloq. Math. 107, No. 1 (2007) 45–56. CR - [13] F. Moricz and Nemeth Z., Statistical extension of classical Tauberian theorems in the case of logarithmic summability, Anal. Math. 40, No. 3 (2014) 231–242. CR - [14] O. Talo and F. Basar, On the Slowly Decreasing Sequences of Fuzzy Numbers, Abstr. Appl. Anal. 2013, (2013) 1–7. CR - [15] E. Yavuz, O. Talo and H. C¸ os¸kun, Cesa`ro summability of integrals of fuzzy-number-valued functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67, No. 2 (2018) 38–49. CR - [16] L. A. Zadeh, Fuzzy sets, Inform. Control 8, (1965) 338–353. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//567505 L1 - https://dergipark.org.tr/en/download/article-file/1069383 ER -