TY - JOUR
ID - 708587
TI - Statistical Deferred Weighted Riemann Summability and Fuzzy Approximation Theorems
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Parida, Priyadarsini
AU - Paikray, Susanta Kumar
AU - Jena, Bidu Bhusan
AD - Department of Mathematics,
Kuntala Kumari Sabat Women's College, Balasore 756003, Odisha,
India.
AD - Department of Mathematics,
Veer Surendra Sai University of Technology,
Burla 768018, Odisha, India.
AD - Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India.
Y1 - 2024
PY - 2024
VL - 21
IS - 1
SP - 327
EP - 345
KW - Fuzzy number valued functions
KW - Riemann integral
KW - Statistical Riemann integral
KW - Deferred weighted mean
KW - Korovkin-type theorems
DO - 10.22130/scma.2023.2000425.1298
N2 - The notion of statistical convergence has fascinated many researchers due mainly to the fact that it is more general than the well-established hypothesis of ordinary (classical) convergence. This work aims to investigate and present (presumably new) the statistical versions of deferred weighted Riemann integrability and deferred weighted Riemann summability for sequences of fuzzy functions. We first interrelate these two lovely theoretical notions by establishing an inclusion theorem. We then state and prove two fuzzy Korovkin-type theorems based on our proposed helpful and potential notions. We also demonstrate that our results are the nontrivial extensions of several known fuzzy Korovkin-type approximation theorems given in earlier works. Moreover, we estimate the statistically deferred weighted Riemann summability rate supported by another promising new result. Finally, we consider several interesting exceptional cases and illustrative examples supporting our definitions and the results presented in this paper.
UR - https://scma.maragheh.ac.ir/article_708587.html
L1 - https://scma.maragheh.ac.ir/article_708587_c3aec703c0edae6ab0d6b80e0148b826.pdf
ER -