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For a positive integer n, applying Schwarz's lemma related to analytic functions w(z) = cnz n + ··· in the open unit disk U, some assertion in a certain lemma which is well-known as Jack's lemma proven by Miller and Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305) is given. Further, by using a certain method of the proof of subordination relation which was discussed by Suridge

Differential subordinations for certain analytic functions missing some coefficients