Publication Details:
«ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա»-ն լույս է տեսնում 1966 թվականից՝ տարին 6 անգամ։
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Title:
Entire functions and their high order difference operators
Creator:
Majumder, S. ; Sarkar, N. ; Pramanik, D.
Contributor(s):
Գլխավոր խմբ․՝ Մ․ Մ․ Ջրբաշյան (1966-1994) ; Ռ․ Վ․ Համբարձումյան (1994-2009) ; Ա․ Ա․ Սահակյան (2010-)
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difference operators ; sharing values ; entire functions
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Abstract:
In this paper, we prove that for a transcendental entire function f of finite order such that λ(f − a) < ρ(f), where a is an entire function and satisfies ρ(a) < ρ(f), n ∈ N, if Δnc f and f share the entire function b satisfying ρ(b) < ρ(f) CM, where c ∈ C satisfies Δnc f ̸≡ 0, then f(z) = a(z)+decz, where d, c are two non-zero constants. In particular, if a = b, then a reduces to a constant. This result improves and generalizes the recent results of Chen and Chen [3], Liao and Zhang [10] and Lü et al. [11] in a large scale. Also we exhibit some relevant examples to fortify our results.
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Երևան
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ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան