Dr. Dennis Agbebaku | Godfrey Okoye University, Nigeria (original) (raw)

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Papers by Dr. Dennis Agbebaku

Novi Sad Journal of Mathematics, Apr 18, 2017

This paper deals with an interpretation of the Order Completion Method for systems of nonlinear p... more This paper deals with an interpretation of the Order Completion Method for systems of nonlinear partial differential equations (PDEs) in terms of suitable differential algebras of generalized functions. In particular, it is shown that certain spaces of generalized functions that appear in the Order Completion Method may be represented as differential algebras of generalized functions. This result is based on a characterization of order convergence of sequences of normal lower semicontinuous functions in terms of pointwise convergence of such sequences. It is further shown how the mentioned differential algebras are related to the nowhere dense algebras introduced by Rosinger, and the almost everywhere algebras considered by Verneave, thus unifying two seemingly different theories of generalized functions. Existence results for generalized solutions of large classes of nonlinear PDEs obtained through the Order Completion Method are interpreted in the context of the earlier nowhere dense and almost everywhere algebras.

Nucleation and Atmospheric Aerosols, 2012

Computational & Applied Mathematics, Feb 14, 2017

Many of the iterative schemes for solving split inclusion and fixed point problems involve step-s... more Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented. Keywords Split variational inclusion problem • Strong convergence • Multi-valued quasi-nonexpansive mappings • Hilbert spaces Mathematics Subject Classification 47H06 • 47H09 • 47J05 • 47J25 Communicated by Carlos Conca.

Novi Sad Journal of Mathematics, Mar 23, 2021

Journal of Mathematics and Statistics, 2020

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach sp... more This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three-step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

J. Math. Comput. Sci., Sep 6, 2020

Theory and Practice of Mathematics and Computer Science Vol. 6, 2021

In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscill... more In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscillator with fractional order derivative. The Homotopy analysis method (HAM) was used to obtain the said analytic solution to the proposed initial valued problem. In order to achieve our goal, the problem was first converted to its augmented equivalent system of equations having the same order. The accuracy of the result obtained was demonstrated with an example and the solution illustrated graphical.

Quaestiones Mathematicae, Nov 7, 2017

It is shown how chains of algebras of generalised functions may be used to construct algebras of ... more It is shown how chains of algebras of generalised functions may be used to construct algebras of generalised functions that are able to deal with larger classes of singularities than each of the constituent algebras in the chain. The general method is applied to a chain of almost everywhere algebras, yielding an algebra that can handle certain densely singular functions. The embedding of the distributions into the mentioned algebra, as well as the existence of solutions of nonlinear PDEs, is considered.

Journal of Mathematical and Computational Science, 2020

We proved strong convergence theorem for approximating split variational inclusion problem and fi... more We proved strong convergence theorem for approximating split variational inclusion problem and fixed point problem for multi-valued nonexpansive mappings in a real Hilbert space. Our iterative scheme is constructed in such a way that its step size does not depend on the norm of the bounded linear operator A.A.A. Our result generalizes some important and recent results in the literature.

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach sp... more This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

It is shown how chains of algebras of generalised functions may be used to construct algebras of ... more It is shown how chains of algebras of generalised functions may be used to construct algebras of generalised functions that are able to deal with larger classes of singularities than each of the constituent algebras in the chain. The general method is applied to a chain of almost everywhere algebras, yielding an algebra that can handle certain densely singular functions. The embedding of the distributions into the mentioned algebra, as well as the existence of solutions of nonlinear PDEs, is considered.

Novi Sad Journal of Mathematics, 2021

Novi Sad Journal of Mathematics, 2017

This paper deals with an interpretation of the Order Completion Method for systems of nonlinear p... more This paper deals with an interpretation of the Order Completion Method for systems of nonlinear partial differential equations (PDEs) in terms of suitable differential algebras of generalized functions. In particular, it is shown that certain spaces of generalized functions that appear in the Order Completion Method may be represented as differential algebras of generalized functions. This result is based on a characterization of order convergence of sequences of normal lower semicontinuous functions in terms of pointwise convergence of such sequences. It is further shown how the mentioned differential algebras are related to the nowhere dense algebras introduced by Rosinger, and the almost everywhere algebras considered by Verneave, thus unifying two seemingly different theories of generalized functions. Existence results for generalized solutions of large classes of nonlinear PDEs obtained through the Order Completion Method are interpreted in the context of the earlier nowhere dense and almost everywhere algebras.

Computational and Applied Mathematics, 2017

Many of the iterative schemes for solving split inclusion and fixed point problems involve step-s... more Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented.

Novi Sad Journal of Mathematics, Apr 18, 2017

This paper deals with an interpretation of the Order Completion Method for systems of nonlinear p... more This paper deals with an interpretation of the Order Completion Method for systems of nonlinear partial differential equations (PDEs) in terms of suitable differential algebras of generalized functions. In particular, it is shown that certain spaces of generalized functions that appear in the Order Completion Method may be represented as differential algebras of generalized functions. This result is based on a characterization of order convergence of sequences of normal lower semicontinuous functions in terms of pointwise convergence of such sequences. It is further shown how the mentioned differential algebras are related to the nowhere dense algebras introduced by Rosinger, and the almost everywhere algebras considered by Verneave, thus unifying two seemingly different theories of generalized functions. Existence results for generalized solutions of large classes of nonlinear PDEs obtained through the Order Completion Method are interpreted in the context of the earlier nowhere dense and almost everywhere algebras.

Nucleation and Atmospheric Aerosols, 2012

Computational & Applied Mathematics, Feb 14, 2017

Many of the iterative schemes for solving split inclusion and fixed point problems involve step-s... more Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented. Keywords Split variational inclusion problem • Strong convergence • Multi-valued quasi-nonexpansive mappings • Hilbert spaces Mathematics Subject Classification 47H06 • 47H09 • 47J05 • 47J25 Communicated by Carlos Conca.

Novi Sad Journal of Mathematics, Mar 23, 2021

Journal of Mathematics and Statistics, 2020

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach sp... more This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three-step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

J. Math. Comput. Sci., Sep 6, 2020

Theory and Practice of Mathematics and Computer Science Vol. 6, 2021

In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscill... more In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscillator with fractional order derivative. The Homotopy analysis method (HAM) was used to obtain the said analytic solution to the proposed initial valued problem. In order to achieve our goal, the problem was first converted to its augmented equivalent system of equations having the same order. The accuracy of the result obtained was demonstrated with an example and the solution illustrated graphical.

Quaestiones Mathematicae, Nov 7, 2017

It is shown how chains of algebras of generalised functions may be used to construct algebras of ... more It is shown how chains of algebras of generalised functions may be used to construct algebras of generalised functions that are able to deal with larger classes of singularities than each of the constituent algebras in the chain. The general method is applied to a chain of almost everywhere algebras, yielding an algebra that can handle certain densely singular functions. The embedding of the distributions into the mentioned algebra, as well as the existence of solutions of nonlinear PDEs, is considered.

Journal of Mathematical and Computational Science, 2020

We proved strong convergence theorem for approximating split variational inclusion problem and fi... more We proved strong convergence theorem for approximating split variational inclusion problem and fixed point problem for multi-valued nonexpansive mappings in a real Hilbert space. Our iterative scheme is constructed in such a way that its step size does not depend on the norm of the bounded linear operator A.A.A. Our result generalizes some important and recent results in the literature.

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach sp... more This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

It is shown how chains of algebras of generalised functions may be used to construct algebras of ... more It is shown how chains of algebras of generalised functions may be used to construct algebras of generalised functions that are able to deal with larger classes of singularities than each of the constituent algebras in the chain. The general method is applied to a chain of almost everywhere algebras, yielding an algebra that can handle certain densely singular functions. The embedding of the distributions into the mentioned algebra, as well as the existence of solutions of nonlinear PDEs, is considered.

Novi Sad Journal of Mathematics, 2021

Novi Sad Journal of Mathematics, 2017

This paper deals with an interpretation of the Order Completion Method for systems of nonlinear p... more This paper deals with an interpretation of the Order Completion Method for systems of nonlinear partial differential equations (PDEs) in terms of suitable differential algebras of generalized functions. In particular, it is shown that certain spaces of generalized functions that appear in the Order Completion Method may be represented as differential algebras of generalized functions. This result is based on a characterization of order convergence of sequences of normal lower semicontinuous functions in terms of pointwise convergence of such sequences. It is further shown how the mentioned differential algebras are related to the nowhere dense algebras introduced by Rosinger, and the almost everywhere algebras considered by Verneave, thus unifying two seemingly different theories of generalized functions. Existence results for generalized solutions of large classes of nonlinear PDEs obtained through the Order Completion Method are interpreted in the context of the earlier nowhere dense and almost everywhere algebras.

Computational and Applied Mathematics, 2017

Many of the iterative schemes for solving split inclusion and fixed point problems involve step-s... more Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented.