Vasile Berinde
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View article: Averaged Iterative Algorithms for Convex Optimization Problems over a Common Fixed-Points Set of Demicontractive Mappings
Averaged Iterative Algorithms for Convex Optimization Problems over a Common Fixed-Points Set of Demicontractive Mappings Open
In this article, we introduce a novel averaged-type iterative scheme designed for solving convex minimization problems over the set of common fixed points of a pair of demicontractive mappings. Under suitable assumptions, we prove that the…
View article: Approaching the split common solution problem for nonlinear demicontractive mappings by means of averaged iterative algorithms
Approaching the split common solution problem for nonlinear demicontractive mappings by means of averaged iterative algorithms Open
We consider new iterative algorithms for solving split common solution problems in the class of demicontractive mappings. These algorithms are obtained by inserting an averaged term into the algorithms previously used in [He, Z. and Du, W-…
View article: An Averaged Halpern-Type Algorithm for Solving Fixed-Point Problems and Variational Inequality Problems
An Averaged Halpern-Type Algorithm for Solving Fixed-Point Problems and Variational Inequality Problems Open
In this paper, we propose and study an averaged Halpern-type algorithm for approximating the solution of a common fixed-point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint in the…
View article: A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems
A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems Open
This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and…
View article: Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring
Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring Open
In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in…
View article: An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems
An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems Open
In this paper we propose and study in the setting of a Hilbert space an averaged Halpern type algorithm for approximating the solution of a common fixed point problem for a couple of nonexpansive and demicontractive mappings with a variati…
View article: New averaged type algorithms for solving split common fixed point problems for demicontractive mappings
New averaged type algorithms for solving split common fixed point problems for demicontractive mappings Open
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used…
View article: An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings
An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings Open
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in th…
View article: An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings
An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings Open
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in li…
View article: Recent developments in the fixed point theory of enriched contractive mappings. A survey
Recent developments in the fixed point theory of enriched contractive mappings. A survey Open
The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings es…
View article: On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces
On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces Open
We give a brief account on a basic result (Lemma \ref{lem2}) which is a very useful tool in proving various convergence theorems in the framework of the iterative approximation of fixed points of demicontractive mappings in Hilbert spaces.…
View article: New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings
New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings Open
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed-point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used…
View article: An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings
An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings Open
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in li…
View article: Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces
Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces Open
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the results obtained in the case of contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approx…
View article: Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces
Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces Open
We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; P˘acurar, M. Approxi…
View article: On approximating fixed points of strictly pseudocontractive mappings in metric spaces
On approximating fixed points of strictly pseudocontractive mappings in metric spaces Open
In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the …
View article: On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces
On a useful lemma that relates quasi-nonexpansive and demicontractive mappings in Hilbert spaces Open
We give a brief account on a basic result (Lemma \ref{lem2}) which is a very useful tool in proving various convergence theorems in the framework of the iterative approximation of fixed points of demicontractive mappings in Hilbert spaces.…
View article: Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects
Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects Open
Demicontractive operators form an important class of nonexpansive type mappings whose study led researchers to the creation of some beautiful results in the framework of metric fixed-point theory. This article aims to provide an overview o…
View article: A heuristic method for solving linear and quasi-linear firstorder partial differential equations
A heuristic method for solving linear and quasi-linear firstorder partial differential equations Open
We present a heuristic method for finding first integrals for linear and quasi-linear first order partial differential equations, when we are often lead to solve exact ordinary differential equations. The method is inspired by the correspo…
View article: Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques
Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques Open
In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappi…
View article: A qualitative analysis of a second-order anisotropic phase-field transition system endowed with a general class of nonlinear dynamic boundary conditions
A qualitative analysis of a second-order anisotropic phase-field transition system endowed with a general class of nonlinear dynamic boundary conditions Open
The paper is concerned with the study of a nonlinear second-order anisotropic phase-field transition system of Caginalp type, subject to nonlinear and in-homogeneous dynamic boundary conditions (in both unknown functions). Under certain hy…
View article: Existence and Approximation of Fixed Points of Enriched φ-Contractions in Banach Spaces
Existence and Approximation of Fixed Points of Enriched φ-Contractions in Banach Spaces Open
We introduce the class of enriched φ-contractions in Banach spaces as a natural generalization of φ-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturat…
View article: Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences
Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences Open
The notion of approximate fixed point sequence , emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool …
View article: A new class of unsaturated mappings: Ćirić-Reich-Rus contractions
A new class of unsaturated mappings: Ćirić-Reich-Rus contractions Open
Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in [Berinde, V.; Păcurar, M. Fixed point theorems for enriched Ćirić-Reich-Rus con…
View article: "Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case"
"Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case" Open
"We prove that the convergence theorems for Mann iteration used for approximation of the fixed points of demicontractive mappings in Hilbert spaces can be derived from the corresponding convergence theorems in the class of quasi-nonexpansi…
View article: "The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects"
"The early developments in fixed point theory on b-metric spaces: a brief survey and some important related aspects" Open
"A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early development…
View article: "Why Pompeiu-Hausdorff metric instead of Hausdorff metric?"
"Why Pompeiu-Hausdorff metric instead of Hausdorff metric?" Open
"The distance between two sets, commonly called Hausdorff metric, is a very important mathematical concept, with plenty of applications in almost all scientific research areas. We suggest in this paper an update of its name as Pompeiu-Haus…
View article: A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings
A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings Open
For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergen…
View article: Maia type fixed point theorems for some classes of enriched contractive mappings in Banach spaces
Maia type fixed point theorems for some classes of enriched contractive mappings in Banach spaces Open
We give some extensions of the beautiful 1968 fixed point theorem of Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes of enriched contractive mappings…
View article: Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators
Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators Open
The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration meth…