scholarly journals Strong convergence theorems of a split common null point problem and a fixed point problem in Hilbert spaces

2020 ◽  
Vol 2 ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Convergence Theorems

scholarly journals Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 167 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Suparat Kesornprom ◽  
Nattawut Pholasa
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.

scholarly journals Weak and Strong Convergence Theorems for Common Attractive Points of Widely More Generalized Hybrid Mappings in Hilbert Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2491
Author(s):  
Panadda Thongpaen ◽  
Attapol Kaewkhao ◽  
Narawadee Phudolsitthiphat ◽  
Suthep Suantai ◽  
Warunun Inthakon
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Common Fixed Point Problem

In this work, we study iterative methods for the approximation of common attractive points of two widely more generalized hybrid mappings in Hilbert spaces and obtain weak and strong convergence theorems without assuming the closedness for the domain. A numerical example supporting our main result is also presented. As a consequence, our main results can be applied to solving a common fixed point problem.

scholarly journals The Split Equality Fixed Point Problem of Demicontractive Operators with Numerical Example and Application

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 902
Author(s):  
Yaqin Wang ◽  
Jinzuo Chen ◽  
Ariana Pitea
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Numerical Example

This paper aims to propose a new reckoning method for solving the split equality fixed point problem of demicontractive operators in Hilbert spaces, and to establish a theorem with regard to the strong convergence of this new scheme. As an application, we also consider quasi-pseudo-contractive operators and obtain a result on the solution to the split equality fixed point problem in the framework of Hilbert spaces. A numerical example is also provided.

Solving split equality common fixed point problem for infinite families of demicontractive mappings

2018 ◽  
Vol 34 (3) ◽  
pp. 321-331
Author(s):  
ADISAK HANJING ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

scholarly journals Strong Convergence Results of Split Equilibrium Problems and Fixed Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li-Jun Zhu ◽  
Hsun-Chih Kuo ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Convergence Results

In this paper, we investigate the split equilibrium problem and fixed point problem in Hilbert spaces. We propose an iterative scheme for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are all pseudocontractive. We show that the suggested scheme converges strongly to a solution of the considered problem.

scholarly journals A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 226 ◽  
Author(s):  
Wachirapong Jirakitpuwapat ◽  
Poom Kumam ◽  
Yeol Cho ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Signal Processing ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Operator Norm ◽  
Point Problem ◽  
Convergence Theorems ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo’s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang’s algorithm, Boikanyo’s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA).

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