Let A denote the class of analytic functions of the form f ( z ) = z + ∑ k = 2 ∞ a k z k in the open unit disk U = { z : | z | < 1 } normalized by f(0) = f'(0) - 1 = 0. We denote by S the subclass of A consisting of functions which are univalent in U.
We denote by K the subclass of A consisting of functions which are convex of order α in U (see, [1, 2]).
We also denote by A the subclass of H [ a, 1 ] with the usual normalization f ( 0 ) = f ′ ( 0 ) − 1 = 0. Let f ( z ) and F ( z ) be members of ℋ.
By S, it is denoted the subclass of the univalent functions in A and by S* and K--the subclasses of S whose members are starlike (with respect to the origin) and convex in U, respectively.
Finally, in terms of a differential operator defined by (1.3) above, let denote the subclass of consisting of functions which satisfy the following inequality: (1.5).
which are analytic and multivalent functions in U. Also, denote by S H ¯ ( n, p ) the subclass of S H ( n, p ) consisting of harmonic functions f = h + g ¯, where h and g are of the form h ( z ) = z p − ∑ k = n + p ∞ a k z k, g ( z ) = − ∑ k = n + p − 1 ∞ b k z k, a k, b k ≥ 0. (2).
We describe as positively conservative the subclass of schemes that by contrast always generate physical solutions from physical data and show that the Godunov method is positively conservative.
(i) For β = 0, we have the subclass of Bazilevic functions defined by Patel [12].
For β = 0, we have the subclass of Bazilevic functions defined by Patel [12].
