On certain non-linear differential monomial sharing non-zero polynomial

S. Majumder; A. Dam

doi:10.37863/umzh.v73i2.99

S. Majumder Raiganj Univ., West Bengal, India
A. Dam North Bengal St. Xavier’s College, West Bengal, India

DOI: https://doi.org/10.37863/umzh.v73i2.99

Ключові слова: Uniqueness, Meromorphic function, small functions, Non-linear differential polynomials and normal family

Анотація

УДК 517.5

Про нелінійний диференціальний одночлен зі спільним ненульовим многочленом

На базі ідеї про нормальні сім'ї функцій вивчається єдиність мероморфних функцій $f$ і $g$ у випадку, коли $f^{n}(\mathcal{L}(f))^{m}-p$ і $g^{n}(\mathcal{L}(g))^{m}-p$ мають спільні значення, де $\mathcal{L}(f)= a_{k}f^{(k)}+a_{k-1} f^{(k-1)}+\ldots +a_{1} f'+a_{0}f$, $a_{k}(\ne 0),a_{k-1},\ldots,a_{1},a_{0}\in\mathbb{C}$, а $p(z)(\not\equiv 0)$ — поліном. Отриманий результат є істотним узагальненням результату з [A. Banerjee, S. Majumder, On certain non-linear differential polynomial sharing a non-zero polynomial, Bol. Soc. Mat. Mex. (2016), https://doi.org/10.1007/s40590-016-0156-0].

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