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SOLVING QUASIMONOTONE SPLIT VARIATIONAL INEQUALITY PROBLEM AND FIXED POINT PROBLEM IN HILBERT SPACES
D. O. Peter,A. A. Mebawondu,G.C. Ugwunnadi,P. Pillay,O.K. Narain 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.1
In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.
ON GENERALIZED (α,β)-NONEXPANSIVE MAPPINGS IN BANACH SPACES WITH APPLICATIONS
F. Akutsah,O.K. Narain 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.4
In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed\ a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.
SOLUTION OF A NONLINEAR DELAY INTEGRAL EQUATION VIA A FASTER ITERATIVE METHOD
J.A. Ugbo,J. Oboyi,M.O. Udo,E.O. Ekpenyong,C.F. Chickwe,O.K. Narain 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.1
In this article, we study the Picard-Ishikawa iterative method for approximating the fixed point of generalized $\alpha$-Reich-Suzuki nonexpanisive mappings. The weak and strong convergence theorems of the considered method are established with mild assumptions. Numerical example is provided to illustrate the computational efficiency of the studied method. We apply our results to the solution of a nonlinear delay integral equation. The results in this article are improvements of well-known results.
EXISTENCE OF SOLUTION OF DIFFERENTIAL EQUATION VIA FIXED POINT IN COMPLEX VALUED b-METRIC SPACES
A. A. Mebawondu,H.A. Abass,M.O. Aibinu,O.K. Narain 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
The concepts of new classes of mappings are introduced in thespaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixedpoints and fixed point results are established in the setting of complete complex valued $b$-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in theframework of a complete complex valued $b$-metric spaces.
L. Mzimela,A. A. Mebawondu,A. Maharaj,C. Izuchukwu,O.K. Narain 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.1
In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of $\rho$-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.
A.E. Ofem,A. A. Mebawondu,C. Agbonkhese,G.C. Ugwunnadi,O.K. Narain 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.1
In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite familyof $\tau$-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.