Results 21 to 30 of about 102 (88)

Krasnoselskii–Mann Iterations: Inertia, Perturbations and Approximation

Journal of Optimization Theory and Applications
Abstract This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure their weak, strong and linear convergence, either matching or improving previous results obtained ...
Daniel Cortild, Juan Peypouquet
openaire   +4 more sources

Modified Fast Inertial‐Type Krasnosel’skii‐Mann Iterative Scheme Involving Asymptotically Nonexpansive Mapping

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
It is our aim to propose a new iterative algorithm with an inertial term involving asymptotically nonexpansive mapping in the framework of Hilbert spaces. Let T : H⟶H be asymptotically nonexpansive mapping with F(T) ≠ ∅ ∅ and let xnn≥0 be defined by xn+1 = σnzn + bn(Tnσnzn − σnzn) + εn, ∀n ≥ 1.
Emmanuel Akaligwo, Micah Osilike, Noemí DeCastro-García, Angel Luis Muñoz Castañeda, David Escudero García, Wiyada Kumam   +5 more
wiley   +1 more source

Some results of the Picard-Krasnoselskii hybrid iterative process

Filomat, 2019
In this paper, we establish the strong convergence and stability results of Picard-Krasnoselskii hybrid iterative process for a general class of contractive-like operators in a hyperbolic space. Additionally, we apply this iterative process to obtain the solution of a functional equation in a Banach space.
openaire   +3 more sources

Exact and Approximate Controllability for Backward Fractional Integro‐Differential Equations With History‐Dependent Operators

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper is devoted to the analysis of controllability for a class of backward fractional integro‐differential equations involving history‐dependent operators, which arise naturally in systems with memory effects. The study begins with the formulation of an appropriate functional framework, within which the concept of approximate controllability is ...
Ghadah Albeladi, Hasanen A. Hammad, Baowei Feng   +2 more
wiley   +1 more source

Picard and Picard-Krasnoselskii iteration methods for generalized proportional Hadamard fractional integral equations

Advances in the Theory of Nonlinear Analysis and its Application, 2022
In the current paper, some existence and uniqueness results for a generalized proportional Hadamard fractional integral equation are established via Picard and Picard-Krasnoselskii iteration methods together with the Banach contraction principle. A simulative example was provided to verify the applicability of the theoretical findings.
openaire   +2 more sources

Stationary and Nonstationary Iterative Methods for Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
The aim of this paper is to present a novel stationary and nonstationary iterative approach for approximating common fixed points of a finite family of generalized nonexpansive mappings in uniformly convex Banach spaces. For the stationary scheme, both strong and weak convergence theorems are established under standard geometric conditions.
Sehar Afsheen, Amna Kalsoom, Faryad Ali, Akbar Azam, John R. Akeroyd   +4 more
wiley   +1 more source

Bounded fixed point sets and Krasnoselskii iterates of Thompson metric nonexpansive maps

, 2023
We consider maps defined on the interior of a normal, closed cone in a real Banach space that are nonexpansive with respect to Thompson's metric. With mild compactness assumptions, we prove that the Krasnoselskii iterates of such maps converge to a fixed point when one exists.
openaire   +3 more sources

Rates of ($T$-)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration

Portugaliae Mathematica
In this paper, we use proof mining methods to compute rates of ( T -)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration associated to a nonexpansive mapping T:X\to X
Paulo Firmino, Laurenţiu Leuştean
openaire   +2 more sources

An Extended Almost Weak Contraction in Relational Metric Space and Applications to Nonlinear Matrix Equations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This manuscript investigates certain fixed point outcomes for an extended almost weak contraction map in a metric space equipped with a locally transitive binary relation. The insights achieved here improve, broaden, solidify and advance a number of noteworthy findings.
Doaa Filali, Esmail Alshaban, Adel Alatawi, Bassam Z. Albalawi, Fahad M. Alamrani, Faizan Ahmad Khan, Smritijit Sen   +6 more
wiley   +1 more source

A Dynamical Systems Approach to Generalized Cayley Inclusion Problem and Convergence Rate Comparison of Iterative Algorithms

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper studies a generalized Cayley inclusion problem governed by a K·,·‐co‐monotone mapping in a real Hilbert space. We show that the proposed inclusion problem can be equivalently reformulated as a fixed‐point problem. Exploiting this equivalence, an inertial extrapolation algorithm is developed to compute solutions of the generalized Cayley ...
Mohd Aftab Alam, Syed Shakaib Irfan, Iqbal Ahmad, Smritijit Sen   +3 more
wiley   +1 more source