Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces byyn=βnSxn+(1-βn)xn,xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and∀n≥0, whereTi:C↦His a nonselfki-strictly pseudocontraction. Under certain approximate conditions, the sequence{xn}converges strongly tox*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.

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Iterative Methods of Weak and Strong Convergence Theorems for the Split Common Solution of the Feasibility Problems, Generalized Equilibrium Problems, and Fixed Point Problems

Journal of Mathematics ◽

10.1155/2020/6689015 ◽

2020 ◽

Vol 2020 ◽

pp. 1-22

Author(s):

Shahram Rezapour ◽

Yuanheng Wang ◽

Seyyed Hasan Zakeri

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Equilibrium Problems ◽

Nonexpansive Mappings ◽

Equilibrium Points ◽

Fixed Point Problems ◽

Weak And Strong Convergence ◽

Iterative Approximation ◽

Common Solution ◽

Generalized Equilibrium

The purpose of this paper is to introduce the extragradient methods for solving split feasibility problems, generalized equilibrium problems, and fixed point problems involved in nonexpansive mappings and pseudocontractive mappings. We establish the results of weak and strong convergence under appropriate conditions. As applications of our three main theorems, when the mappings and their domains take different types of cases, we can obtain nine iterative approximation theorems and corollas on fixed points, variational inequality solutions, and equilibrium points.

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A novel iterative approach for solving common fixed point problems in Geodesic spaces with convergence analysis

Carpathian Journal of Mathematics ◽

10.37193/cjm.2021.02.01 ◽

2021 ◽

Vol 37 (2) ◽

pp. 145-160

Author(s):

THANATPORN BANTAOJAI ◽

CHANCHAL GARODIA ◽

IZHAR UDDIN ◽

NUTTAPOL PAKKARANANG ◽

PANU YIMMUANG

Keyword(s):

Fixed Point ◽

Iterative Method ◽

Common Fixed Point ◽

Rate Of Convergence ◽

Convergence Analysis ◽

Nonexpansive Mappings ◽

Fixed Point Problems ◽

Iterative Approach ◽

Mild Conditions ◽

New Iterative Method

In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.

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Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Mathematics ◽

10.3390/math8040462 ◽

2020 ◽

Vol 8 (4) ◽

pp. 462

Author(s):

Bing Tan ◽

Zheng Zhou ◽

Songxiao Li

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Hilbert Spaces ◽

Nonexpansive Mappings ◽

Fixed Point Problems ◽

Convergence Theorems ◽

Numerical Examples ◽

Infinite Dimensional

We investigated two new modified inertial Mann Halpern and inertial Mann viscosity algorithms for solving fixed point problems. Strong convergence theorems under some fewer restricted conditions are established in the framework of infinite dimensional Hilbert spaces. Finally, some numerical examples are provided to support our main results. The algorithms and results presented in this paper can generalize and extend corresponding results previously known in the literature.

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