Browsing by Author "Opoola, T. O."
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Item Iterated integral transforms of Caratheodory functions and their applications to analytic and univalent functions(Tamkang University, 2006) Babalola, Kunle Oladeji; Opoola, T. O.In this paper, we develop and study some integral transforms of Caratheodory functions. We apply the transforms to study certain other classes of analytic and univalent functions both to obtain new results and provide new proofs of some known onesItem On coefficient bounds of a subclass of univalent functions(Nigerian Mathematical Society, 2004) Opoola, T. O.; Babalola, Kunle Oladeji; Fadipe-Joseph, O. A.; Rauf, K.Let T(_n^α)(β) denote the class of functions f(z)=z+∑_(k=2)^∞▒〖a_k z^k 〗, univalent and analytic in the unit disk U={z∈ C:|z|<1} such that Re(D^n [〖f(z)〗^α])/z^α>β, z∈U,n∈{0}∪N,α>0,0≤β<1 and D^n is the salagean differential operator, in this paper, we establish some coefficient bounds for functions of the class T(_n^α)(β).Item On the coefficient of a certain class of analytic functions(Nova Science Publishers Inc., New York, 2008) Babalola, Kunle Oladeji; Opoola, T. O.In this paper, we solve certain coefficient problems for functions of the class T(_n^α)(β) introduced in [7] by Opoola. In particular, for some index α>0 we obtain sharp bounds for the coefficients of these functions. Furthermore we give some rough estimate of the general coefficient bounds using the logarithmic coefficient approach. We also prove the analogue of the well known Fekete-Szego theorem for this class of functionsItem Radius problems for a certain class of analytic functions(Nova Science Publishers Inc., New York, 2008) Babalola, Kunle Oladeji; Opoola, T. O.In this paper, we determine the radii of starlikeness and convexity of functions of the class T(_n^α)(β) introduced in [3] by Opoola. It is well known that for n=0, this class consists largely of analytic functions which are not necessarily univalent in the unit disk. For this case n=o, the radius of univalence is indicated by the sufficiency of starlikenessItem A sharp inclusion theorem for a certain class of analytic functions defined by the Salagean derivative(Lebanese University, Hadath, Lebanon, 2007) Babalola, Kunle Oladeji; Opoola, T. O.In this short note we employ the Briot-Bouquet differential subordination to determine the best possible inclusion relation within a certain family of analytic functions defined by the Salagean derivativeItem Some applications of a lemma concerning analytic functions having positive real part in the unit disk(Lebanese University, Hadath, Lebanon, 2007) Opoola, T. O.; Babalola, Kunle OladejiIn this paper we give some applications of a lemma of Babalola and Opoola [3], which is a classical extension of an earlier one by Lewandowski, Miller, Zlotkiewicz [9]. The applications were given via a new generalization of some well known subclasses of univalent functions, and they unify many known results