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EXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS VIA F-CONTRACTION MAPPINGS IN METRIC SPACES
Komi Afassinou,Ojen Kumar Narain 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
The purpose of this paper is to present some sufficient conditions for the existence and uniqueness of solutions of the nonlinear Hammerstein integral equations and thetwo-point boundary value problems for nonlinear second-ordinary differential equations. Toestablish this, we introduce the generalized Suzuki-(α, β)-F-contraction and the generalized(α, β)-F-contraction in the framework of a metric space and establish some fixed point results. The results obtained in this work provide extension as well as substantial generalizationand improvement of several well-known results on fixed point theory and its applications.
Komi Afassinou,Ojen Kumar Narain,Oluwaseun Elizabeth Otunuga 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.3
The goal of this paper is to introduce a modified Halpern iterative algorithm for approximating solutions of split monotone variational inclusion, variational inequality and fixed point problems of an infinite families of multi-valued type-one demicontractive mappings in the framework of real Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution of split monotone variational inclusion, variational inequality problems and fixed point problem for countable family of multi-valued type-one demicontractive mappings. The iterative algorithm employed in this paper is designed in such a way that it does not require the knowledge of operator norm. Lastly, we give some consequences of our main result and give application of one of the consequences to split minimization problem. The result presented in this paper extends and generalizes some related results in literature.
Hammad Anuoluwapo Abass,Akindele Adebayo Mebawondu,Ojen Kumar Narain,Jong Kyu Kim 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.3
In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.
Austine Efut Ofem,Godwin Chidi Ugwunnadi,Ojen Kumar Narain,Jong Kyu Kim 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.3
In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition $(E)$ in hyperbolic spaces. The concepts weak $w^2$-stability involving three multi-valued almost contraction mappings are considered. Several strong and $\triangle$-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.