Equivalence Between Nonlinear Complementarity Problem and Fixed Point Problem

In this paper, using the classic Banach fixed point theorem, we study the nonlinear complementarity problem for a class of monotone operators in real Hilbert space.

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A quadratically convergent algorithm for the generalized nonlinear complementarity problem

Information Science and Management Engineering ◽

10.2495/isme131912 ◽

2013 ◽

Author(s):

Kaixun Chen

Keyword(s):

Complementarity Problem ◽

Nonlinear Complementarity Problem ◽

Nonlinear Complementarity ◽

Convergent Algorithm

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Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽

10.3390/sym13020158 ◽

2021 ◽

Vol 13 (2) ◽

pp. 158

Author(s):

Liliana Guran ◽

Monica-Felicia Bota

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Boundary Value ◽

Fixed Point Problem ◽

Point Problem ◽

Existence Of A Solution ◽

Shadowing Property ◽

Limit Shadowing ◽

Type Boundary ◽

Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

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Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽

10.3390/sym13071161 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1161

Author(s):

Jinhua Zhu ◽

Jinfang Tang ◽

Shih-sen Chang ◽

Min Liu ◽

Liangcai Zhao

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Equilibrium Problems ◽

Fixed Point Problem ◽

Finite Family ◽

Variational Inclusion ◽

Point Problem ◽

Hadamard Manifolds ◽

Inclusion Problems ◽

Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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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 ◽

Common Fixed Point Problem ◽

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.

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The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

Fixed Point Theory and Applications ◽

10.1186/s13663-020-00686-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Yuanheng Wang ◽

Xiuping Wu ◽

Chanjuan Pan

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Banach Spaces ◽

Optimization Problems ◽

Nonexpansive Mappings ◽

Fixed Point Problem ◽

Iteration Algorithm ◽

Point Problem ◽

Asymptotically Nonexpansive ◽

Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

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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 ◽

Common Fixed 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.

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