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Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

Panigrahi S, Basu R.

Journal of Applied Analysis

2015

Vol. 21, nr 2

109--121

In this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [5]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.

Fixed coefficients for certain subclasses of starlike functions with negative coefficients

Aouf M., Al-Dohiman A.

Demonstratio Mathematica

2005

Vol. 38, nr 3

551--565

The main object of this paper is to study the class T*n,c(alfa,beta) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T*n,c(alfa,beta). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.