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BERINDE TYPE RESULTS VIA SIMULATION FUNCTIONS IN METRIC SPACES
Komi Afassinou,Jong Kyu Kim 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.3
In this paper, we introduce coincidence point theorems for Beride type contraction mappings via simulation functions and obtain some sufficient axioms for the existence and uniqueness of coincidence point for such class of mappings in the setting of metric spaces.
EXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS VIA F-CONTRACTION MAPPINGS IN METRIC SPACES
Komi Afassinou,Ojen Kumar Narain 경남대학교 수학교육과 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 수학교육과 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.