1. A generalization of Lappan's five point theorem.
- Author
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Singh, Virender and Lal, Banarsi
- Subjects
MEROMORPHIC functions ,GENERALIZATION - Abstract
In this paper, we prove the following result: Let F be a family of meromorphic functions on a domain D and let S = φ i : 1 ≤ i ≤ 5 be a set of five distinct meromorphic functions on D. If for each f ∈ F and z 0 ∈ D , there is a constant M > 0 such that f # (z 0) ≤ M whenever f (z 0) = φ (z 0) for some φ ∈ S and if f (z 0) ≠ φ (z 0) for all φ ∈ S whenever φ i (z 0) = φ j (z 0) for some i , j ∈ 1 , 2 , 3 , 4 , 5 with i ≠ j , then F is normal on D. Further we extend this result to the case where the set S contains fewer functions. In particular, our result generalizes the most significant theorem of Lappan (i.e. Lappan's five point theorem). [ABSTRACT FROM AUTHOR]
- Published
- 2023
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