scholarly journals Generalized AOR Method for Solving Absolute Complementarity Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Javed Iqbal ◽  
Khalida Inayat Noor ◽  
E. Al-Said
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Equivalent Formulation ◽  
Existence Of A Solution ◽  
Absolute Value ◽  
New Class ◽  
Aor Method ◽  
The Absolute

We introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation is used to discuss the existence of a solution of the absolute value complementarity problem. A generalized AOR method is suggested and analyzed for solving the absolute the complementarity problems. We discuss the convergence of generalized AOR method for theL-matrix. Several examples are given to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction.

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

Symmetry ◽  
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.

scholarly journals Some Proximal Methods for Solving Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam Noor ◽  
Zhenyu Huang
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Methods ◽  
Proximal Point ◽  
Equivalent Formulation ◽  
New Methods ◽  
Special Cases ◽  
Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems

2019 ◽  
Vol 26 (1) ◽  
pp. 63-78
Author(s):  
Kaleem Raza Kazmi ◽  
Rehan Ali
Keyword(s):  
Banach Space ◽  
Projection Method ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Solution Set ◽  
Common Element ◽  
Monotone Mappings ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Hybrid Projection Method

Abstract The aim of this paper is to consider a generalized mixed variational-like inequality problem and prove a Minty-type lemma for its related auxiliary problems in a real Banach space. We prove the existence of a solution of these auxiliary problems. Further, we prove some properties of a solution set of generalized mixed variational-like inequality problems. Furthermore, we use a hybrid projection method to find a common element of a solution set of a system of unrelated generalized mixed variational-like inequality problems for generalized relaxed α-monotone mappings and the set of fixed points of a common fixed point problem for a family of generalized asymptotically quasi-ϕ-nonexpansive mappings in a reflexive, uniformly smooth and strictly convex Banach space.

scholarly journals Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Dual Space ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Existence Of A Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We study and establish the existence of a solution for a generalized mixed equilibrium problem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3365-3379 ◽  
Author(s):  
Z. Ahmadi ◽  
R. Lashkaripour ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Complete Metric Spaces ◽  
New Class ◽  
Constraint Inequalities ◽  
Weaker Conditions

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

scholarly journals On a complementarity problem associated with nondifferentiable programming

1984 ◽  
Vol 25 (3) ◽  
pp. 419-430 ◽  
Author(s):  
B. D. Craven ◽  
B. Mond ◽  
J. Parida
Keyword(s):  
Existence Theorem ◽  
Stationary Point ◽  
Complementarity Problem ◽  
Optimal Solution ◽  
Nondifferentiable Programming ◽  
Regularity Conditions ◽  
Point Problem ◽  
Nonlinear Program ◽  
Existence Of A Solution

AbstractThis paper deals with the question of the existence of a solution to the stationary-point problem corresponding to a given nonlinear nondifferentiable program. An existence theorem for the stationary-point problem is presented under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the nonlinear program.

scholarly journals Existence of common fixed point for b-metric rational type contraction

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1413-1429 ◽  
Author(s):  
Mujahid Abbas ◽  
Imran Chema ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Contractive Condition ◽  
Existence Of A Solution ◽  
Contractive Mappings ◽  
Common Fixed Point Problem ◽  
Rational Type ◽  
Type Contraction

The necessary conditions for existence of a common fixed point of two mappings satisfying generalized b-order contractive condition in the setting of a partially ordered b-complete b-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized b-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.

scholarly journals GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES

2008 ◽  
Vol 49 (4) ◽  
pp. 525-531
Author(s):  
ALI P. FRAJZADEH ◽  
MUHAMMAD ASLAM NOOR
Keyword(s):  
Variational Inequalities ◽  
Vector Space ◽  
Complementarity Problems ◽  
Vector Spaces ◽  
Kkm Mapping ◽  
Existence Of A Solution ◽  
Topological Vector Spaces ◽  
New Class ◽  
Special Cases ◽  
New Type

AbstractIn this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.

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