Mathematics - Scholarly Publications

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    Open Access
    On Weighted Spaces Without a Fundamental Sequence of Bounded Sets
    (Hindawi Publishing Corporation, 2002-09-21) Olaleru, J.O
    The problem of countably quasi-barrelledness of weighted spaces of continuous functions, of which there are no results in the general setting of weighted spaces, is tackled in this paper. This leads to the study of quasi-barrelledness of weighted spaces in which, unlike that of Ernst and Schnettler (1986), though with a similar approach, we drop the assumption that the weighted space has a fundamental sequence of bounded sets. The study of countably quasi-barrelledness of weighted spaces naturally leads to definite results on the weighted (DF)-spaces for those weighted spaces with a fundamental sequence of bounded sets.
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    Open Access
    Weighted locally convex spaces of measurable functions
    (Revista Colombiana de Matematicas, 2004) Olaleru, J.O
    In this paper, we make a study of weighted locally convex spaces of measurable functions parallel to the studies of weighted locally convex spaces of continuous functions which has been a subject of intense research for decades. With Lp; 1 < p < 1, spaces as our motivation, the completeness and inductive limits of those spaces are studied including their relationship with the weighted spaces of continuous functions leading to new results and generalizations of results true for Lp spaces.
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    Open Access
    The Fixed Points of Certain Discontinuous Operator on Locally Convex Spaces
    (Asian Network for Scientific Information, 2006) Olaleru, J.O
    The fixed point properties of four classes of operators mapping a metrisable locally convex space into itself are considered. These classes include contraction, and non-expansive mappings, discontinuous operators for certain parameter values of the classes. The existence of fixed points are proved for these classes of mappings under some conditions. Furthermore, a cone ordering scheme is devised for one of these classes, while another is shown to have open mapping properties. All these results generalize the work of Derrick and Nova from Banach spaces to metrisable locally convex spaces.
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    Open Access
    An Extension of Gregus Fixed Point Theorem
    (Hindawi Publishing Corporation, 2006-12-17) Olaleru, J.O; Akewe, H
    Let C be a closed convex subset of a complete metrizable topological vector space (X,d) and T :C→C a mapping that satisfies d(Tx,Ty)≤ad(x,y)+bd(x,Tx)+cd(y,Ty)+ ed(y,Tx)+ fd(x,Ty) for all x,y∈C, where 0
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    Open Access
    A comparison of Picard and Mann Iterations for Quasi-Contraction Maps
    (Fixed Point Theory Journal, 2007) Olaleru, J.O
    For a class of quasi-contractive operators defined on an arbitrary Banach space, it has been shown that the Picard iteration technique converges faster than the Mann iteration technique. In this paper we make a comparison of the Picard and Mann iterations with respect to their convergence rate for a more general class of operators called quasi-contractions in metrizable topological vector spaces. It was observed that the Picard iteration converges faster than the Mann iteration for this class of maps. This answers the question posed by Berinde in his paper.
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    Open Access
    An Extension of Gregus Fixed Point Theorem
    (Hindawi Publishing Corporation, 2007) Olaleru, J.O; Akewe, H
    Let C be a closed convex subset of a complete metrizable topological vector space (X,d) and T : C → C a mapping that satisfies d(Tx,Ty) ≤ ad(x, y) + bd(x,Tx) + cd(y,Ty) +ed(y,Tx) + f d(x,Ty) for all x, y ∈ C, where 0 < a < 1, b ≥ 0, c ≥ 0, e ≥ 0, f ≥ 0, and a + b + c + e + f = 1. Then T has a unique fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper.In addition, we use the Mann iteration to approximate the fixed point of T.
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    Open Access
    On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators
    (Hindawi Publishing Corporation, 2010-01) Akewe, H; Olaleru, J.O
    We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized.
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    Open Access
    Budget Deficits, External Debt and Economic Growth in Nigeria
    (World Scientific Publishing Company, 2010-09) Osinubi, T.S; Dauda, R.O.S; Olaleru, O.E
    The necessity for governments to borrow in order to finance deficit budgets has led to the development of external debt. This study examines how the use of budget deficits as an instrument of stabilization leads to the accumulation of external debt with the attending effects on growth in Nigeria between 1970 and 2003. By synthesizing a relationship between budget deficits and external debt the study shows the implications on economic growth of conducting a fiscal policy within the contexts of debt stabilization and debt sustainability. The results of the econometric analysis confirm the existence of the debt Laffer curve and the nonlinear effects of external debt on growth in Nigeria. The study concludes that if debt-financed budget deficits are operated in order to stabilize the debt ratio at the optimum sustainable level debt overhang problems would be avoided and the benefits of external borrowing would be maximized.
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    Open Access
    The Equivalence of Jungck-Type Iterations for Generalized Contractive-Like Operators in a Banach Space
    (2011) Olaleru, J.O; Akewe, H
    We show that the convergences of Jungck, Jungck- Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep itera- tion processes are equivalent for a class of generalized contractive- like operators defined on a Banach space. Our results are general- izations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.
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    Open Access
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    Open Access
    A linear multi-step hybrid methods with continuous coefficient for solving stiff ordinary differential equation
    (2011) OA Akinfenwa, SN Jator, NM Yao
    A four-step Continuous Block Hybrid Method (CBHM) with four non-step points of order (9, 9, 10, 9, 9, 9, 9, 9)T is proposed for the direct solution of the 1st order Initial Value Problems (IVPs). The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The stability properties of the methods are discussed and the stability region shown. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form shows that it is attractive for solutions of stiff problems.
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    Open Access
    An eighth order backward differentiation formula with continuous coefficients for stiff ordinary differential equations
    (2011-02-27) O Akinfenwa, S Jator, N Yoa
    A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.
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    Open Access
    On the convergence of modified three-step iteration process for generalized contractive-like operators
    (2012) Olaoluwa, H; Akewe, H
    In this paper, we introduce a new Jungck-three step iterative scheme and call it modified three-step iteration process. A strong conver- gence theorem is proved using this iterative process for the class of generalized contractive-like operators introduced by Olatinwo [14] and Bosede [3] respec- tively, in a Banach space. The results obtained in this paper improve and generalize among others, the results of Bosede [3], Olatinwo and Imoru [13], Shaini and Singh [16], Jungck [6] and Berinde [2].
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    Open Access
    Coupled fixed point theorems of integral type mappings in cone metric spaces
    (2012-06-07) Olaleru, J.O; Okeke, G.A; Akewe, H
    In this paper, we prove some coupled fixed point theorems in cone metric spaces. Furthermore, we introduce and prove the integral version of coupled fixed point theorems in cone metric spaces. Our results unify, extend and generalize the known results on coupled fixed point theorems in cone metric spaces
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    Open Access
    Strong Convergence and Stability of Jungck-Multistep-SP Iteration for Generalized Contractive-Like Inequality Operators
    (CSCanada, 2012-06-11) Akewe, H
    We introduce the Jungck-multistep-SP iteration and prove some convergence as well as stabiilty results for a pair of weakly compatible generalized contractive- like inequality operators defined on a Banach space. As corollaries, the results show that the Jungck-SP and Jungck-Mann iterations can also be used to approximate the common fixed points of such operators. The results are improvements, generalizations and extensions of the work of Chugh and Kumar (2011). Consequently, several results in literature are generalized.
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    Open Access
    On The Stability of Continuous Block Backward Differentiation Formula For Solving Stiff Ordinary Differential Equations.
    (2012-07) OA Akinfenwa, SN Jator, NM Yao
    This paper focuses on the stability regions of numerical methods and to demonstrate its suitability for the solution stiff ordinary differential equations. In particular, the purpose of this paper is to generate the stability region for methods of Continuous Block Backward Differentiation Formulae (CBBDF) that simultaneously generate the approximate solution of the stiff ODEs. The practical importance of the methods is established for the stability regions since it cover the whole of the negative half-complex plane.
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    Open Access
    Fixed Point Theorems For Mappings Satisfying General Contractive Condition Of Integral Type In G-Metric Spaces
    (2012-07-18) Akewe, H
    Abstract In this paper, we prove some theorems on fixed and common fixed points for mappings satisfying general contractive condition of integral type in a complete G-metric space. Our results are extensions of the results of Debashis Dey, Anamika Ganguly and Mantu Saha [2] and generalizations of several results in the literature including the results of Branciari
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    Open Access
    Convergence Theorems on Asymptotically Generalized Φ-Hemicontractive Mappings in the Intermediate Sense
    (Hikari Ltd, 2013) Olaleru, J.O; Okeke, G.A; Akewe, H
    In this study, we introduce two classes of nonlinear mappings, the class of asymptotically generalized Φ-hemicontractive mappings in the intermediate sense and asymptotically generalized Φ-pseudocontractive mappings in the intermediate sense; and prove the convergence of Mann type iterative scheme with errors to their fixed points. Our results generalize the results of Chang et al. [4], Chidume and Chidume [5] and Kim et al. [8] among others.
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    Open Access
    Some Fixed point results on ordered G-Partial metric spaces.
    (ICASTOR Journal of Mathematical Sciences., 2013) Eke, K.S.; Olaleru, J.O
    We introduce a new concept of generalized metric space called a G- partial metric space and prove the fixed point of certain contraction maps defined on the ordered G- metric spaces. Our work extends some works in literature.
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    Open Access
    Existence of Fixed Points of Asymptotically Generalized Φ-Hemicontractive Mappings in the Intermediate Sense
    (Hikari Ltd, 2013) Olaleru, J.O; Okeke, G.A
    Let E be a real Banach space, C be a nonempty closed convex subset of E and T : C → C be a continuous generalized Φ-pseudocontractive mapping, Xiang [Chang He Xiang, Fixed point theorem for general- ized Φ-pseudocontractive mappings, Nonlinear Analysis 70 (2009) 2277- 2279] proved that T has a unique fixed point in C. It is our purpose in this study to extend the results of Xiang [11] to the class of asymptoti- cally generalized Φ-hemicontractive mappings in the intermediate sense, recently introduced by Okeke, Olaleru and Akewe [6].