Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem

Maldar, Samet

doi:10.1007/s12190-021-01593-y

Cited by 5 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problems of existence, uniqueness and other properties of solutions of special forms of BVP (1.1)-(1.2) and its variants have been studied by several researchers under variety of hypotheses by using different techniques (as in [1,3,11,12,15,16,17,18,19,20,21,31,32]). Recently, S. Soltuz and T. Grosan [36] have studied the special version of equation (1.1).…”

Section: Introductionmentioning

confidence: 99%

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

TIDKE¹,

PATIL²

2022

CMI

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

TIDKE¹,

PATIL²

2022

CMI

View full text Add to dashboard Cite

show abstract

“…For the solution in question, it is necessary to include the problem to be solved in an operator class under appropriate conditions. For this reason, many researchers have defined new iteration algorithms in the classical sense with the claim that they have better convergence speed, and the properties of these algorithms such as convergence, data dependency, and stability have been examined (see [11][12][13][14][15][16][17][18][19]).…”

Section: Introductionmentioning

confidence: 99%

New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities

Maldar

2022

Symmetry

Self Cite

View full text Add to dashboard Cite

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions.

show abstract

General semi-implicit approximations with errors for common fixed points of nonexpansive-type operators and applications to Stampacchia variational inequality

Lan

Zhang

2022

Comp. Appl. Math.

View full text Add to dashboard Cite

It is meaningful and valuable to find common fixed points of different nonexpansive-type operators, which are associated with variational inequalities, integral equations, image process and other optimization problems in real life. The purpose of this paper is to suggest and consider a class of general semi-implicit iterative methods involving semi-implicit rule and inaccurate computing errors, which extend the iterative algorithm introduced by Ali et al. in 2020. Using Liu’s lemma, we analyze convergence and stability of the new iterative approximations for common fixed points of three different nonexpansive-type operators. Furthermore, we provide convergence rates of the new iterations and some numerical examples to illustrate the efficiency and stability of the new iterative schemes. As an application of our main results presented in this paper, we use the proposed iterative schemes to solve the known Stampacchia variational inequality.

show abstract

Iterative algorithms of generalized nonexpansive mappings and monotone operators with application to convex minimization problem

Cited by 5 publications

References 27 publications

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities

General semi-implicit approximations with errors for common fixed points of nonexpansive-type operators and applications to Stampacchia variational inequality

Contact Info

Product

Resources

About