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Strong convergence theorems for fixed point of multi-valued map**s in Hadamard spaces
With the help of CN-inequality, we study fixed point of multi-valued map**s with closed bounded images and establish some strong convergence...
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Testing and Non-linear Preconditioning of the Proximal Point Method
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence...
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Fixed Point Problems
In this chapter, we deal with the well-posedness of fixed point problems of the form...
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A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes
This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25 (4), 829–858,
2017 ) for computing a zero of the... -
Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems
The common fixed points problem requires finding a point in the intersection of fixed points sets of a finite collection of operators. Quickly...
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Approximate solution of zero point problem involving H-accretive maps in Banach spaces and applications
In this manuscript, we introduce two iterative methods for finding the common zeros of two H -accretive map**s in uniformly smooth and uniformly...
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A Green’s Function Iterative Approach for the Solution of a Class of Fractional BVPs Arising in Physical Models
The aim of this study is to present an alternative approach for the numerical solution of a wide class of fractional boundary value problems (FBVPs)...
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Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically,...
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On solving variational inequalities defined on fixed point sets of multivalued map**s in Banach spaces
We are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive...
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A parallel extragradient-like projection method for unrelated variational inequalities and fixed point problems
In this paper, we introduce a parallel extragradient-like projection algorithm for finding a common solution of a system of unrelated variational...
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Strong convergence of inertial algorithms for solving equilibrium problems
In this paper, we introduce several inertial-like algorithms for solving equilibrium problems (EP) in real Hilbert spaces. The algorithms are...
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The inertial relaxed algorithm with Armijo-type line search for solving multiple-sets split feasibility problem
The multiple-sets split feasibility problem is the generalization of split feasibility problem, which has been widely used in fuzzy image...
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Accelerated Subgradient Extragradient Methods for Variational Inequality Problems
In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based...
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A splitting algorithm for finding fixed points of nonexpansive map**s and solving equilibrium problems
We consider the problem of finding a fixed point of a nonexpansive map**, which is also a solution of a pseudo-monotone equilibrium problem, where...
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Iterative algorithm for a family of generalized strictly pseudononspreading map**s in CAT(0) spaces
The main purpose of this paper is to introduce a new map** given by a finite family of generalized strictly pseudononspreading map**s. Also, we...
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On A Proximal-Point Algorithm For Solving the Minimization Problem and Common Fixed-Point Problem in Cat(k) Spaces
We propose a new modified proximal-point algorithm in the setting of CAT(1) spaces, which can be used to solve the minimization problem and the...
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Some characterizations of Reich and Chatterjea type nonexpansive map**s
We introduce two types of map**s, namely Reich type nonexpansive and Chatterjea type nonexpansive map**s, and derive some sufficient conditions...
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Convergence Theorems and Convergence Rates for the General Inertial Krasnosel’skiǐ–Mann Algorithm
The authors [13] introduced a general inertial Krasnosel’skiǐ–Mann algorithm: $$ \left\{...
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Proximal Gradient Methods for Machine Learning and Imaging
Convex optimization plays a key role in data sciences. The objective of this work is to provide basic tools and methods at the core of modern...