Let be a transcendental meromorphic function, and let be a continuous and nondecreasing function tends to as . We denote by the set of all meromorphic functions satisfying , where . The author considers the uniqueness problem on the class defined by a proximate order with some angular conditions. Concerning the proximate order, see e.g., C. Chuang [Sci. Sin. 10, 171–181 (1961; Zbl 0102.04704)].
Let be a domain in , and be a set of complex numbers. Denote . The author defines , and , where and the algebraic equation has nomultiple roots.
It is mentioned that the following is proved. Let and suppose that . Let , where and . Suppose that in the definition of , and for some ,
If and , , then .