A new self-adaptive accelerated method for generalized split system of common fixed-point problem of averaged mappings

Weak Convergence Theorem ◽

Theoretical Application ◽

Averaged Mappings ◽

Split System ◽

AbstractThe purpose of this paper is to propose a new inertial self-adaptive algorithm for generalized split system of common fixed point problems of finite family of averaged mappings in the framework of Hilbert spaces. The weak convergence theorem of the proposed method is given and its theoretical application for solving several generalized problems is presented. The behavior and efficiency of the proposed algorithm is illustrated by some numerical tests.

Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

International Journal of Computer Mathematics ◽

10.1080/00207160.2019.1622687 ◽

2019 ◽

Vol 97 (7) ◽

pp. 1431-1443 ◽

Cited By ~ 4

Author(s):

Raweerote Suparatulatorn ◽

Anchalee Khemphet ◽

Phakdi Charoensawan ◽

Suthep Suantai ◽

Narawadee Phudolsitthiphat

Keyword(s):

Fixed Point ◽

Image Restoration ◽

Common Fixed Point ◽

Adaptive Algorithm ◽

Fixed Point Problem ◽

Point Problem ◽

Restoration Problem ◽

A new self-adaptive method for the split equality common fixed-point problem of quasi-nonexpansive mappings

Optimization ◽

10.1080/02331934.2020.1830400 ◽

2020 ◽

pp. 1-22

Author(s):

Jing Zhao ◽

Dingfang Hou ◽

Xinglong Wang

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Nonexpansive Mappings ◽

Adaptive Method ◽

Fixed Point Problem ◽

Point Problem ◽

A new self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in Hilbert spaces

Numerical Algorithms ◽

10.1007/s11075-021-01144-3 ◽

2021 ◽

Author(s):

Simeon Reich ◽

Truong Minh Tuyen ◽

Nguyen Thi Thu Thuy ◽

Mai Thi Ngoc Ha

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Hilbert Spaces ◽

Adaptive Algorithm ◽

Fixed Point Problem ◽

Point Problem ◽

Improved self-adaptive iterative algorithms for the split equality common fixed-point problem of firmly quasi-nonexpansive operators

Journal of Nonlinear Functional Analysis ◽

10.23952/jnfa.2020.41 ◽

2020 ◽

Vol 2020 (1) ◽

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Iterative Algorithms ◽

Fixed Point Problem ◽

Point Problem ◽

Nonexpansive Operators ◽

An accelerated viscosity algorithm with self-adaptive step size for split common fixed point problem

International Mathematical Forum ◽

10.12988/imf.2021.912298 ◽

2021 ◽

Vol 16 (4) ◽

pp. 179-194

Author(s):

L.S. Zhang ◽

Z.L. Ma ◽

J.F. Xiong

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Problem ◽

Point Problem ◽

Step Size ◽

Adaptive Step Size ◽

Adaptive Step ◽

Self-Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings

Journal of Applied Mathematics and Physics ◽

10.4236/jamp.2019.710150 ◽

2019 ◽

Vol 07 (10) ◽

pp. 2187-2199

Author(s):

Xinhong Chen ◽

Yanlai Song ◽

Jianying He ◽

Liping Gong

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Adaptive Algorithms ◽

Fixed Point Problem ◽

Point Problem ◽

An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

Journal of Inequalities and Applications ◽

10.1186/s13660-019-2203-7 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Meixia Li ◽

Xueling Zhou ◽

Haitao Che

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Split Feasibility Problem ◽

Fixed Point Problem ◽

Feasibility Problem ◽

Iteration Algorithm ◽

Point Problem ◽

Contractive Mappings ◽

Significant Generalization

Abstract In this paper, we are concerned with the split equality common fixed point problem. It is a significant generalization of the split feasibility problem, which can be used in various disciplines, such as medicine, military and biology, etc. We propose an alternating iteration algorithm for solving the split equality common fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings and prove that the sequence generated by the algorithm converges weakly to the solution of this problem. Finally, some numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽

10.3390/math9040372 ◽

2021 ◽

Vol 9 (4) ◽

pp. 372

Author(s):

Nishu Gupta ◽

Mihai Postolache ◽

Ashish Nandal ◽

Renu Chugh

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Prior Knowledge ◽

Iterative Algorithm ◽

Fixed Point Problem ◽

Null Point ◽

Operator Norm ◽

Point Problem ◽

Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.