Papers by Chinedu Izuchukwu
Computational and Applied Mathematics
The main purpose of this paper is to propose and study a two-step inertial anchored version of th... more The main purpose of this paper is to propose and study a two-step inertial anchored version of the forward–reflected–backward splitting algorithm of Malitsky and Tam in a real Hilbert space. Our proposed algorithm converges strongly to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. It involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration; a feature that is absent in many other available strongly convergent splitting methods in the literature. Finally, we perform numerical experiments involving image restoration problem and compare our algorithm with known related strongly convergent splitting algorithms in the literature.
Fixed Point Theory, 2020
The main purpose of this paper is to introduce a modified inertial forward-backward splitting met... more The main purpose of this paper is to introduce a modified inertial forward-backward splitting method and prove its strong convergence to a zero of the sum of two accretive operators in real uniformly convex Banach space which is also uniformly smooth. We then apply our results to solve variational inequality problem and convex minimization problem. We also give a numerical example of our algorithm to show that it converges faster than the un-accelerated modified forwardbackward algorithm.
Fixed Point Theory, 2022
In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman ... more In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman quasi-nonexpansive mappings in reflexive Banach spaces. Using the Bregman technique together with a Halpern iterative algorithm, we approximate a solution of split common fixed point problem and sum of two monotone operators in reflexive Banach spaces. We establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this article is design in such a way that it does not require prior knowledge of operator norm and we do not employ Fejer monotinicity condition in the strategy of proving our convergence theorem. We apply our result to solve variational inequality and convex minimization problems. The result discuss in this paper extends and complements many related results in literature.
Boletim da Sociedade Paranaense de Matemática, 2022
In this paper, we obtain sufficient conditions for the existence of a unique fixed point of $T$- ... more In this paper, we obtain sufficient conditions for the existence of a unique fixed point of $T$- mean nonexpansive mapping and an integral type of $T$- mean nonexpansive mapping. We also obtain sufficient conditions for the existence of coincidence point and common fixed point for a Jungck-type mean nonexpansive mapping in the frame work of a complete metric space. Some examples of $T$-mean nonexpansive and Jungck-type mean nonexpansive mappings which are not mean nonexpansive mapping are given. The result obtained generalizes corresponding results in this direction in the literature.
Advances in Operator Theory, 2020
In this paper, we introduce an iterative algorithm for approximating a common solution of Split E... more In this paper, we introduce an iterative algorithm for approximating a common solution of Split Equality Monotone Inclusion Problem (SEMIP) and Split Equality Fixed Point Problem (SEFPP) in p-uniformly convex Banach spaces which are also uniformly smooth. Under standard and mild assumptions of monotonicity and right Bregman strongly condition of the SEMIP-and SEFPP-associated mappings, we establish the strong convergence of the scheme. Finally, we applied our result to study the convex minimization problem (CMP) and Equilibrium Problem. Our result complements and extends some recent results in literature. Keywords Monotone inclusion problem Á Fixed point problem Á Right Bregman strongly nonexpansive mapping Á Maximal monotone mapping Á Resolvent operators Mathematics Subject Classification 47H09 Á 47H10 Á 49J20 Á 49J40 Tusi Mathematical Research Group
International Journal of Nonlinear Analysis and Applications, 2020
In this paper, we introduce a new iterative algorithm of inertial form for approximating the solu... more In this paper, we introduce a new iterative algorithm of inertial form for approximating the solution of Split Variational Inclusion Problem (SVIP) involving accrective operators in Banach space. Motivated by the inertial technique, we incorporate the inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity of the SVIP associated mappings, we establish the weak convergence of the sequence generated by our algorithm. Some applications and numerical example are presented to illustrate the performance of our method as well as comparing it with the non-inertial version.
Proyecciones (antofagasta), 2021
In this paper, we introduce a modified Ishikawa-type proximal point algorithm for approximating a... more In this paper, we introduce a modified Ishikawa-type proximal point algorithm for approximating a common solution of minimization problem, monotone inclusion problem and fixed point problem. We obtain a strong convergence of the proposed algorithm to a common solution of finite family of minimization problem, finite family of monotone inclusion problem and fixed point problem for asymptotically demicontractive mapping in Hadamard spaces. Numerical example is given to illustrate the applicability of our main result. Our results complement and extend some recent results in literature.
International Journal of Nonlinear Analysis and Applications, 2020
The aim of this paper is to introduce a new class of mappings called $(alpha, beta)$-Berinde-$var... more The aim of this paper is to introduce a new class of mappings called $(alpha, beta)$-Berinde-$varphi$-contraction mappings and to establish some fixed point results for this class of mappings in the frame work of metric spaces. Furthermore, we applied our results to the existence of solution of second order differential equations and the existence of a solution for the following nonlinear integral equation: begin{align*} x(t)=g(t)+int_a^bM(t,s)K(t,x(s))ds, end{align*} where $M:[a,b]times [a,b]tomathbb{R}^+,$ $K:[a,b]times mathbb{R}to mathbb{R}$ and $ g:[a,b]to mathbb{R}$ are continuous functions. Our results improve, extend and generalize some known results in the literature. In particular, our main result is a generalization of the fixed point result of Pant cite{ran}.
Methods of Functional Analysis and Topology, 2020
In this paper, we introduce some classes of mappings called the TAC-SuzukiBerinde type F -contrac... more In this paper, we introduce some classes of mappings called the TAC-SuzukiBerinde type F -contraction and TAC-Suzuki-Berinde type rational F -contraction in the frame work of b-metric spaces and prove some fixed point results for these classes of mappings. As an application, we establish the existence of a solution for the following nonlinear integral equation:
Demonstratio Mathematica, 2020
Our main interest in this article is to introduce and study the class of θ-generalized demimetric... more Our main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.
Revista de la Unión Matemática Argentina, 2021
We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mappi... more We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mapping and the resolvent of a convex function in a Hadamard space. We obtain a strong convergence of the proposed algorithm to a minimizer of a convex function which is also a fixed point of a Lipschitz hemicontractive non-self mapping. Furthermore, we give a numerical example to illustrate and support our method. Our proposed method improves and extends some recent works in the literature.
Revista de la Unión Matemática Argentina, 2020
We introduce a viscosity iterative algorithm for approximating a common solution of a modified sp... more We introduce a viscosity iterative algorithm for approximating a common solution of a modified split generalized equilibrium problem and a fixed point problem for a quasi-pseudocontractive mapping which also solves some variational inequality problems in real Hilbert spaces. The proposed iterative algorithm is constructed in such a way that it does not require the prior knowledge of the operator norm. Furthermore, we prove a strong convergence theorem for approximating the common solution of the aforementioned problems. Finally, we give a numerical example of our main theorem. Our result complements and extends some related works in the literature.
Axioms, 2020
In this paper, we propose and study an iterative algorithm that comprises of a finite family of i... more In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature.
Journal of Applied Analysis, 2020
In this paper, we introduce and study an Ishikawa-type iteration process for the class of general... more In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.
Journal of Mathematics, 2020
We introduce a new algorithm (horizontal algorithm) in a real Hilbert space, for approximating a ... more We introduce a new algorithm (horizontal algorithm) in a real Hilbert space, for approximating a common fixed point of a finite family of mappings, without imposing on the finite family of the control sequences ςnin=1∞i=1N, the condition that ∑i=1Nςni=1, for each n≥1. Furthermore, under appropriate conditions, the horizontal algorithm converges both weakly and strongly to a common fixed point of a finite family of type-one demicontractive mappings. It is also applied to obtain some new algorithms for approximating a common solution of an equilibrium problem and the fixed point problem for a finite family of mappings. Our work is a contribution to ongoing research on iteration schemes for approximating a common solution of fixed point problems of a finite family of mappings and equilibrium problems.
Journal of Mathematics, 2019
The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, ... more The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.
Journal of Inequalities and Applications, 2019
In this paper, we introduce a new viscosity-type iteration process for approximating a common sol... more In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 201...
Applied General Topology, 2019
The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, compris... more The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.
Novi Sad Journal of Mathematics, 2018
The purpose of this paper is to introduce a proximal iterative algorithm for the approximation of... more The purpose of this paper is to introduce a proximal iterative algorithm for the approximation of a common solution of finite families of split minimization problem and a fixed point problem in the framework of Hilbert space. Using our iterative algorithm, we prove a strong convergence theorem for approximating a common solution of finite families of split minimization problem and a fixed point problem of nonexpansive mapping. Moreover, our result complements and extends some related results in literature.
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Papers by Chinedu Izuchukwu