Results 11 to 20 of about 741 (181)

Partially nonexpansive mappings

Advances in the Theory of Nonlinear Analysis and its Application, 2022
It is defined a class of generalized nonexpansive mappings, which properly contains those defined by Suzuki in 2008, and that preserves some of its fixed point results.
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On the Weak Relatively Nonexpansive Mappings in Banach Spaces

Fixed Point Theory and Applications, 2010
In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give two examples which are weak relatively ...
Yongfu Su, Yongchun Xu
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Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications

Abstract and Applied Analysis, 2012
The purpose of this paper is to present the notion of weak relatively nonexpansive multi-valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces.
Jingling Zhang, Yongfu Su, Qingqing Cheng   +2 more
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Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications

Journal of Applied Mathematics, 2012
The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive ...
Sumei Ai, Yongfu Su
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Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space [PDF]

Journal of Hyperstructures
In this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized
Omprash Sahu, Amitabh Banerjee
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On Firmly Nonexpansive Mappings [PDF]

Proceedings of the American Mathematical Society, 1991
The author proves the following. Let X be a uniformly convex Banach space, \(C=C_ 1\cup C_ 2\cup...\cup C_ n\) a union of nonempty, bounded, closed and convex subsets of X, and T: \(C\to C\) a mapping such that \[ \| Tx-Ty\| \leq \| (1-\lambda)(x-y)+\lambda (Tx-Ty)\| \quad (x,y\in C), \] for some \(\lambda\in (0,1)\). Then T has a fixed point in C.
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Demiclosedness Principles for Generalized Nonexpansive Mappings [PDF]

Journal of Optimization Theory and Applications, 2020
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments for the weak convergence of the shadow sequence generated by the Douglas-Rachford algorithm. We provide extensions
Sedi Bartz, Rubén Campoy, Hung M. Phan
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Convergence Theorems for a Maximal Monotone Operator and a 𝑉-Strongly Nonexpansive Mapping in a Banach Space

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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Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

Abstract and Applied Analysis, 2015
Let E be a smooth Banach space with a norm ·. Let V(x,y)=x2+y2-2 x,Jy for any x,y∈E, where ·,· stands for the duality pair and J is the normalized duality mapping. We define a V-strongly nonexpansive mapping by V(·,·).
Hiroko Manaka
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On a Class of Generalized Nonexpansive Mappings

Mathematics, 2020
In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.
Simeon Reich, Alexander J. Zaslavski
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