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- ItemOpen AccessOn Weighted Spaces Without a Fundamental Sequence of Bounded Sets(Hindawi Publishing Corporation, 2002-09-21) Olaleru, J.O
Show more 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.Show more - ItemOpen AccessWeighted locally convex spaces of measurable functions(Revista Colombiana de Matematicas, 2004) Olaleru, J.O
Show more 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.Show more - ItemOpen AccessThe Fixed Points of Certain Discontinuous Operator on Locally Convex Spaces(Asian Network for Scientific Information, 2006) Olaleru, J.O
Show more 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.Show more - ItemOpen AccessAn Extension of Gregus Fixed Point Theorem(Hindawi Publishing Corporation, 2006-12-17) Olaleru, J.O; Akewe, H
Show more 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 0Show more - ItemOpen AccessA comparison of Picard and Mann Iterations for Quasi-Contraction Maps(Fixed Point Theory Journal, 2007) Olaleru, J.O
Show more 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.Show more - ItemOpen AccessAn Extension of Gregus Fixed Point Theorem(Hindawi Publishing Corporation, 2007) Olaleru, J.O; Akewe, H
Show more 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.Show more - ItemOpen AccessOn Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators(Hindawi Publishing Corporation, 2010-01) Akewe, H; Olaleru, J.O
Show more 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.Show more - ItemOpen AccessBudget Deficits, External Debt and Economic Growth in Nigeria(World Scientific Publishing Company, 2010-09) Osinubi, T.S; Dauda, R.O.S; Olaleru, O.E
Show more 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.Show more - ItemOpen AccessThe Equivalence of Jungck-Type Iterations for Generalized Contractive-Like Operators in a Banach Space(2011) Olaleru, J.O; Akewe, H
Show more 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.Show more - ItemOpen AccessA linear multistep hybrid methods with continuous coefficient for solving stiff ordinary differential equation(2011) OA Akinfenwa, SN Jator, NM Yao
Show more - ItemOpen AccessA linear multi-step hybrid methods with continuous coefficient for solving stiff ordinary differential equation(2011) OA Akinfenwa, SN Jator, NM Yao
Show more 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.Show more - ItemOpen AccessAn eighth order backward differentiation formula with continuous coefficients for stiff ordinary differential equations(2011-02-27) O Akinfenwa, S Jator, N Yoa
Show more 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.Show more - ItemOpen AccessOn the convergence of modified three-step iteration process for generalized contractive-like operators(2012) Olaoluwa, H; Akewe, H
Show more 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].Show more - ItemOpen AccessCoupled fixed point theorems of integral type mappings in cone metric spaces(2012-06-07) Olaleru, J.O; Okeke, G.A; Akewe, H
Show more 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 spacesShow more - ItemOpen AccessStrong Convergence and Stability of Jungck-Multistep-SP Iteration for Generalized Contractive-Like Inequality Operators(CSCanada, 2012-06-11) Akewe, H
Show more 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.Show more - ItemOpen AccessOn The Stability of Continuous Block Backward Differentiation Formula For Solving Stiff Ordinary Differential Equations.(2012-07) OA Akinfenwa, SN Jator, NM Yao
Show more 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.Show more - ItemOpen AccessFixed Point Theorems For Mappings Satisfying General Contractive Condition Of Integral Type In G-Metric Spaces(2012-07-18) Akewe, H
Show more 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 BranciariShow more - ItemOpen AccessConvergence Theorems on Asymptotically Generalized Φ-Hemicontractive Mappings in the Intermediate Sense(Hikari Ltd, 2013) Olaleru, J.O; Okeke, G.A; Akewe, H
Show more 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.Show more - ItemOpen AccessSome Fixed point results on ordered G-Partial metric spaces.(ICASTOR Journal of Mathematical Sciences., 2013) Eke, K.S.; Olaleru, J.O
Show more 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.Show more - ItemOpen AccessExistence of Fixed Points of Asymptotically Generalized Φ-Hemicontractive Mappings in the Intermediate Sense(Hikari Ltd, 2013) Olaleru, J.O; Okeke, G.A
Show more 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].Show more