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    Open Access
    On the Radius of Starlikeness and Convexity of Certain Subclass of Analytic Functions
    (2011) Makinde, D. O.; Opoola, T. O.
    In this paper, we investigate the radius of starlikeness and convexity of the function f(z)
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    Open Access
    A Characterization of Analyticity Using Cauchy Integral Formula
    (2010) Makinde, D. O.
    In this paper, we obtain a general characterization of analyticity of function of a complex variable using Cauchy integral formula.
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    Open Access
    On a Certain Integral Univalent Operator
    (2011) Makinde, D. O.
    In this paper, author proves some properties of a certain integral operator.
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    Open Access
    Construction of Higher Orthogonal Polynomials through a New Inner Product <.,.>p in a Countable Real Lp-space
    (2005) Oyadare, 'Femi O.
    This research work places a new and consistent inner product <.,.>p on a countable family of the real Lp function spaces, proves generalizations of some of the inequalities of the classical inner product for <.,.>p provides a construction of a species of Higher Orthogonal Polynomials in these inner-product-admissible function spaces, and ultimately brings us to a study of the Generalized Fourier Series Expansion in terms of these polynomials. First, the reputation of this new inner product is established by the proofs of various inequalities and identities, all of which are found to be generalizations of the classical inequalities of functional analysis. Thereafter two orthogonalities of <.,.>p which coincide at p = 2) are defined while the Gram-Schmidt orthonormalization procedure is considered and lifted to accommodate this product, out of which emerges a set of higher orthogonal polynomials in Lp{-1, 1} that reduce to the Legendre Polynomials at p = 2. We argue that this inner product provides a formidable tool for the investigation of Harmonic Analysis on the real Lp function spaces for p other than p = 2, and a revisit of the various fields where the theory of inner product spaces is indispensable is recommended for further studies.
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    Open Access
    Thermal Instability in Reactive Viscous Plane Poiseuille/Couette Flows for Two Extreme Thermal Boundary Conditions
    (2009) Ajadi, Suraju Olusegun
    The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for critically using the variational method technique. The problem is characterized by two parameters: the Nusselt number (N) and the dynamic parameter. We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.