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    An algorithm for choosing best shape parameter for numerical solution of partial differential equation via inverse multiquadric radial basis function
    (Open Journal of Mathematical Sciences (OMS), 2020-04-30) Kazeem Issa; Sulaiman M. Hambali; Jafar Biazar
    Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
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    Cubic Spline Chebyshev Polynomial Approximation for Solving Boundary Value Problems
    (Earthline Journal of Mathematical Sciences, 2024-07-04) A.K.Jimoh; M.H.Sulaiman; A.S.Muhmmed
    In this work, a Chebyshev polynomial spline function is derived and used to approximate the solution of the second order two-point boundary value problems of variable coefficients with the associated boundary conditions. In deriving the method, the cubic spline Chebyshev polynomial approximation, S(x) is made to satisfy certain conditions for continuity and smoothness of functions. Numerical examples are presented to illustrate the applications of this method. The solution, y(x) of these examples are obtained at some nodal points in the interval of consideration. The absolute errors in each example are estimated, and the comparison of exact values, and approximate values by the present method and other methods in literature at the nodal points are presented graphically. The comparison shows that the proposed method produces better results than Approaching Spline Techniques and collocation method.
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    Flux-Hardy Inequalities with Optimal Constants via Divergence and Rearrangements
    (Unilorin Press, 2024) Anise M. A.∗, Soleye S. L. and Rauf K.
    We develop sharp Hardy-type inequalities for boundary flux functionals generated by dilations of a fixed smooth set in R^n. The method combines the divergence theorem with rearrangement bounds to reduce flux estimates to one-dimensional Hardy averages. Directional, divergence-form, and multi-flux inequalities are obtained in arbitrary dimension with the optimal constant and sharpness is shown by explicit near-extremizing constructions.
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    RESULTS ON CONDENSED KANNAN-TYPE 2-CYCLIC MAP IN b-METRIC SPACES
    (Scik, 2026-03-30) MUSA S.A. , WAHAB O.T., ALIU T.O., FATAI M.O., ANISE M.A.
    Some authors recently proposed a condensed Kannan-type map that can solve nonlinear problems with unique and non-unique solutions. However, these findings may not address all situations involving inexact spaces. This study presents a strategy for proving fixed points of Kannan-type 2-cyclic contractions by condensation in inexact spaces, commonly referred to as b-metric spaces. We further extend the findings to study fixed points of trivially cyclic mappings. With the aid of examples comprising cyclic and trivially cyclic mappings, we validate all hypotheses of this study. The results show that the condensed cyclic Kannan-type map is more elaborate than the previous Kannan-type cyclic maps in the literature, solves problems with the inexact structures, and ensures unique and non-unique fixed points
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    Extension of Hermite-Hadamard Companions of Riemann-Liouville Inequality Type with k-fractional Integrals
    (Ik press, 2026) M. A. Anise and K. Rauf
    The previous research on Hermite-Hadamard inequalities focused on classical h-convex, s-convex and new companions of RiemannLiouville k-fractional integrals type by means of generalized convex functions, and generalized mid point forms were left unexplored. This present study deals with the derivation of some flexible convexity classes that depend on a generating function. As a result, important nonlinear behaviours coordinated convex function within the usual linear setting. However, little research has been established on through relative semi-convex, relative h-convex and relative g-convex functions.