Abstract
In the present paper, we propose an analytical approach for solving the 3D unsteady-state boundary-value problem for the second-order parabolic equation with the second and third types boundary conditions in two-layer rectangular parallelepipedic domain.
Highlights
Let A be the class of the functions in the form (1.1) U z : z 1which are analytic in the open unit diskWe denote by S the subclass of A consisting of functions which are univalent in U
Which are analytic in the open unit disk
Which are analytic in the open unit disk U [2]
Summary
Gao and Zhou [1], have researched the class ( , ) and showed some mapping properties of this subclass. Brannan and Taha [8], obtained estimates on the initial coefficients a2 and a3 for the functions in the classes of bi-starlike functions of order and bi-convex functions of order. Despite the numerous studies mentioned above, the problem of estimating the coefficients an (n 2, 3,...) for the general class functions is still open [12]. Someone can see the Fekete-Szegö problem for the classes of starlike functions of order and convex functions of order at special cases in the paper of Orhan, et al [22]. Zaprawa [24], Zaprawa [25], have studied on FeketeSzegö problem for some subclasses of bi-univalent functions In special cases, he gave the Fekete-Szegö problem for the subclasses bi-starlike functions of order and bi-convex functions of order. Motivated by the aforementioned works, we define a new subclass of bi-univalent functions as follows
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