Results 1 to 10 of about 9,111 (245)

Fixed points of weakly K-nonexpansive mappings and a stability result for fixed point iterative process with an application

Journal of Inequalities and Applications, 2022
In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness.
Sayantan Panja, Kushal Roy, Marija V. Paunović, Mantu Saha, Vahid Parvaneh   +4 more
doaj   +1 more source

Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems

Journal of Mathematics, 2021
In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point.
Laishram Shanjit, Yumnam Rohen, K. Anthony Singh   +2 more
doaj   +1 more source

A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Journal of Inequalities and Applications, 2009
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of ...
Klin-eam Chakkrid, Suantai Suthep
doaj   +2 more sources

A Modified Proximal Point Algorithm and Some Convergence Results

Journal of Mathematics, 2021
In this paper, the convergence to minimizers of a convex function of a modified proximal point algorithm involving a single-valued nonexpansive mapping and a multivalued nonexpansive mapping in CAT(0) spaces is studied and a numerical example is given to
Shengquan Weng, Dingping Wu, Zengfu Chao
doaj   +1 more source

Convergence theorems for total asymptotically nonexpansive mappings in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces

Fixed Point Theory and Algorithms for Sciences and Engineering, 2023
The purpose of this paper is to study the convergence theorems in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces with k > 0 $k > 0$ for total asymptotically nonexpansive mappings which are essentially wider than nonexpansive mappings, asymptotically ...
Shih-sen Chang, Liangcai Zhao, Min Liu, Jinfang Tang   +3 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source