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Inertial Viscosity Iterative Method for Solving Pseudo-monotone Variational Inequality Problems and fixed point Problems

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Acta Mathematica Sinica,English Series 2022年第5期38卷 937-952页

作者： Gang CAI Qiao Li DONG Yu PENG School of Mathematics Science Chongqing Normal UniversityChongqing 401331P.R.China College of Science Civil Aviation University of ChinaTianjin 300300P.R.China

In this paper,we investigate a new inertial viscosity extragradient algorithm for solving variational inequality problems for pseudo-monotone and Lipschitz continuous operator and fixed point problems for quasi-nonexpansive mappings in real Hilbert *** convergence theorems are obtained under some appropriate conditions on the ***,we give some numerical experiments to show the advantages of our proposed *** results obtained in this paper extend and improve some recent works in the literature.

关键词： Extragradient method variational inequality fixed point strong convergence quasi-nonexpansive mapping

A HYBRID VISCOSITY APPROXIMATION METHOD FOR A COMMON SOLUTION OF A GENERAL SYSTEM OF VARIATIONAL INEQUALITIES,AN EQUILIBRIUM PROBLEM,AND fixed point PROBLEMS

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Journal of Computational Mathematics 2023年第1期41卷 153-172页

作者： Maryam Yazdi Saeed Hashemi Sababe Young Researchers and Elite Club Malard BranchIslamic Azad UniversityMalardIran Department of mathematical and statistical sciences University of AlbertaEdmontonCanada Young Researchers and Elite ClubMalard BranchIslamic Azad UniversityMalardIran

In this paper,we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities,an equilibrium problem,and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert *** prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the ***,we apply our main result for ***,we give two numerical results to show the consistency and accuracy of the scheme.

关键词： Equilibrium problem Iterative method fixed point Variational inequality

On Some Novel fixed point Results for Generalized F-Contractions in b-Metric-Like Spaces with Application

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Computer Modeling in Engineering & Sciences 2023年第4期135卷 673-686页

作者： Kastriot Zoto Ilir Vardhami Dusan Bajovic Zoran D.Mitrovic Stojan Radenovic Department of Mathematics and Computer Sciences Faculty of Natural SciencesUniversity of GjirokastraGjirokastra6001Albania Department of Mathematics Faculty of Natural SciencesUniversity of TiranaTirana1001Albania Faculty of Electrical Engineering University of Banja LukaBanja Luka78000Bosnia and Herzegovina Department of Mathematics Faculty of Mechanical EngineeringUniversity of BelgradeBeograd11120Serbia

The focusofourwork is on themost recent results infixedpoint theoryrelated *** variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and *** particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like *** main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is *** an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

关键词： (φ,F)-contraction (s,q,φ,F)-contraction b-metric-like space fixed point

Some new fixed point results under constraint inequalities in comparable complete partially ordered Menger PM-spaces

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Applied Mathematics(A Journal of Chinese Universities) 2022年第4期37卷 494-512页

作者： WU Zhao-qi ZHANG Lin ZHU Chuan-xi YUAN Cheng-gui ^Department of Mathematics Nanchang UniversityNanchang 330031China Institute of Mathematics Hangzhou Dianzi UniversityHangzhou 310018China Department of Mathematics Swansea UniversitySingleton ParkSA28PPUK

In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger *** obtain some new results which generalize many known ones in the ***,we derive some consequent results and give an example to illustrate our main result.

关键词： Menger PM-space fixed point constraint inequalities partial order implicit contraction

Modified Subgradient Extragradient Method for Variational Inequality Problems and fixed point Problems

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Journal of Harbin Institute of Technology(New Series) 2022年第5期29卷 11-19页

作者： Xiaoyin Li Hongwei Liu Jiangli Cheng Dongyao Zhang School of Mathematics and Statistics Xidian UniversityXi’an 710126China

Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert *** order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial ***,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz ***,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.

关键词： inertial method fixed point variational inequality strong convergence subgradient extragradient method

fixed point RESULTS ON METRIC-TYPE SPACES

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Acta Mathematica Scientia 2014年第4期34卷 1237-1253页

作者： Monica COSENTINO Peyman SALIMI Pasquale VETRO Dipartimento di Matematica e Informatica Universita degli Studi di PalermoVia Archirafi3490123 PalermoItaly Young Researchers and Elite Club Rasht BranchIslamic Azad UniversityRashtIran

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an applica... 详细信息

关键词： metric-type space fixed point common fixed point Suzuki type mappings cone metric space integral equation

fixed point theorems for better admissible multimaps on Abstract convex spaces

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 55-62页

作者： LIU Xue-wen ZHANG Yue TAN Ren-xin School of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China School of Mathematics and Computer Science Chongqing Normal University Chongqing China

In this paper, a better admissible class B＋ is introduced and a new fixed point theorem for better admissible multimap is proved on abstract convex spaces. As a consequence, we deduce a new fixed point theorem on abs... 详细信息

关键词： Multimap fixed point abstract convex space better admissible class.

fixed point THEOREMS OF LOCAL CONTRACTION MAPPINGS ON MENGER SPACES

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Applied Mathematics and Mechanics(English Edition) 1991年第4期12卷 363-372页

作者：方锦暄 Department of Mathematics Nanjing Normal University Nanjing

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.

关键词： probabilistic metric space Menger space e-chainable local contraction mapping fixed point

fixed point Separating Congruences on Double MS-Algebras

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Acta Mathematica Sinica,English Series 1998年第1期14卷 99-104页

作者： Fang Jie Department of Mathematics, Zhongshan University, Guangzhou, 510275, China Mathematical Institute, University of St Andrews. St Andrews, Fife, KY16 9SS, Scotland, U. K. 中山大学数学系广东广州

Here we show that there exists a greatest fixed point separating congruence denoted by ψ on a double MS-algebra (L;~0, +), Some properties of ψ under certain conditions on fixed point complete and fixed point distri... 详细信息

关键词： Double MS-algebra fixed point Separating congruence