On Lemniscate Starlikeness of the Solution of General Differential Equations

Saiful R. Mondal ()
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Saiful R. Mondal: Department of Mathematics and Statistics, Collage of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia

Mathematics, 2022, vol. 10, issue 18, 1-10

Abstract: In this article, we derived conditions on the coefficient functions a ( z ) and b ( z ) of the differential equations y ″ ( z ) + a ( z ) y ′ ( z ) + b ( z ) y ( z ) = 0 and z 2 y ″ ( z ) + a ( z ) z y ′ ( z ) + b ( z ) y ( z ) = 0 , such their solution f ( z ) with normalization f ( 0 ) = 0 = f ′ ( 0 ) − 1 is starlike in the lemniscate domain, equivalently z f ′ ( z ) / f ( z ) ≺ 1 + z . We provide several examples with graphical presentations for a clear view of the obtained results.

Keywords: lemniscate starlike; differential equations; subordination; Bessel functions; hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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