We define Baker omitted value, in short bov, of an entire or meromorphic function f in the complex plane as an omitted value for which there exists r 0 > 0 such that for each ball D r (a) centred at a and with radius r satisfying 0 < r < r 0 , every component of the boundary of f −1 (D r (a)) is bounded. The existence and some dynamical implications of bov is investigated in this article. The bov of a function is the only asymptotic value. An entire function has bov if and only if the image of every unbounded curve is unbounded. It follows that an entire function has bov whenever it has a Baker wandering domain. A sufficient condition for existence of bov of meromorphic functions is also proved. Functions with bov have at most one completely invariant Fatou component. Some counter examples are provided and problems are proposed for further investigation. ARTICLE HISTORY

No abstract

We study the change of dynamics of transcendental meromorphic functions f? = ? ez/z+1 for z ? C when ? varies on the negative real axis. It is shown that there is a ?^ such that the Fatou set of f? is empty for ? < ?^ whereas the Fatou set is an invariant parabolic basin corresponding to a real rationally indifferent fixed point x^ if ? = ?^ . In fact, the Fatou set is an invariant attracting basin of a real negative fixed point ?? if ?^ < ? < 0. Also the dynamics of fn? for n ? 2 at the fixed points is investigated for different values of ?. As a generalization of f?, we observed some dynamical issues for the class of entire maps F?,a,m(z) = ?(z+a)m exp(z) where ?, a ? C and m ? N.

No abstract

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic cofficients of finite logarithmic order in the unit disc. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.