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Abstract
In this paper, some new fuzzy di¤erential subordinations obtained
by using the integral operator Im
: An ! Anintroduced in [13] are obtained.
Results & Lemmas (2)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Theorem 11.
Theorem 11. Let q be univalent in U and let and be analytic functions in a domain D containing q(U), with (w) 6= 0, when w 2 q(U). Let F:…
Theorem 11. Let q be univalent in U and let and be analytic functions in a domain D containing q(U), with (w) 6= 0, when w 2 q(U). Let F : U ! [0; 1]; F(z) = 1 1 + jzj; z 2 U: Set Q(z) = zq0(z) [q(z)]; h(z) = [q(z)] + Q(z); and suppose that we have (i) Q is starlike; (ii) Re zh0(z) Q(z) = Re 0[q(z)] [q(z)] + zQ0(z) Q(z)
Theorem 12.
Theorem 12. Let q be univalent in U, with q(0) = 1, q(z) 6= 0, z 2 U, and let : C ! C, (w) = w and: C ! C, (w) = 1 w, (w) 6= 0, w 6= 0.…
Theorem 12. Let q be univalent in U, with q(0) = 1, q(z) 6= 0, z 2 U, and let : C ! C, (w) = w and : C ! C, (w) = 1 w, (w) 6= 0, w 6= 0. Let F : U ! [0; 1]; F(z) = 1 1 + jzj; z 2 U: Set Q(z) = zq0(z) [q(z)]; h(z) = [p(z)] + Q(z) = [p(z)] + zq0(z) [q(z)] and suppose that we have (j) Re 0[q(z)] [q(z)] > 0; (jj) Re 1 + zq00(z)
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