The Monotone Contraction Mapping Theorem [PDF]
Journal of Mathematics, 2020 In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.
Joseph Frank Gordon
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Some Results on Fixed Points for Monotone Inward Mappings in Geodesic Spaces [PDF]
مجلة بغداد للعلوم, 2022 In this article, the partially ordered relation is constructed in geodesic spaces by betweeness property, A monotone sequence is generated in the domain of monotone inward mapping, a monotone inward contraction mapping is a monotone Caristi inward ...
khalid Abed Jassim
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A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces [PDF]
Abstract and Applied Analysis, 2013 We introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012), and we generalize the variational inclusion involving the -monotone mapping.
Jinlin Guan, Changsong Hu
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Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping [PDF]
Journal of Applied Mathematics, 2014 We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone
Xian Wang, Jun-min Chen, Hui Tong
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Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings [PDF]
Fixed Point Theory and Applications, 2009 We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method.
Chakkrid Klin-eam, Suthep Suantai
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A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces [PDF]
Journal of Mathematics, 2019 In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space.
F. U. Ogbuisi +2 more
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Strong Convergence Theorems for Maximal Monotone Operators with Nonspreading Mappings in a Hilbert Space [PDF]
Abstract and Applied Analysis, 2012 We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mapping T and the solution sets of zero of a maximal monotone mapping and an α-inverse strongly monotone mapping in a Hilbert space. Manaka
Hongjie Liu +2 more
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Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces [PDF]
Journal of Inequalities and Applications, 2010 The purpose of this paper is to present a regularization variant of the inertial proximal point algorithm for finding a common element of the set of solutions for a variational inequality problem involving a hemicontinuous monotone mapping A and for a ...
Nguyen Buong, Jong Kyu Kim
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On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping [PDF]
Abstract and Applied Analysis, 2013 We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive ...
Marwan Amin Kutbi, Wutiphol Sintunavarat
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Convergence Theorems for a Maximal Monotone Operator and a 𝑉-Strongly Nonexpansive Mapping in a Banach Space [PDF]
Abstract and Applied Analysis, 2010 Let E be a smooth Banach space with a norm ‖⋅‖. Let 𝑉(𝑥,𝑦)=‖𝑥‖2+‖𝑦‖2−2⟨𝑥,𝐽𝑦⟩ for any 𝑥,𝑦∈𝐸, where ⟨⋅,⋅⟩ stands for the duality pair and J is the normalized duality mapping.
Hiroko Manaka
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