Fixed Point Theory and Algorithms for Sciences and Engineering
ESCI-ISI
2730-5422
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Các bài báo tiêu biểu
On the nonlinear Hadamard-type integro-differential equationAbstract This paper studies uniqueness of solutions for a nonlinear Hadamard-type integro-differential equation in the Banach space of absolutely continuous functions based on Babenko’s approach and Banach’s contraction principle. We also include two illustrative examples to demonstrate the use of main theorems.
Tập 2021 Số 1 - 2021
Solving nonlinear and dynamic programming equations on extended b-metric spaces with the fixed-point technique Abstract In this article, we present an approach to solve a wide range of nonlinear equations formulated in extended b-metric spaces based on a new fixed-point theorem on these spaces. This research effort was motivated by challenges arising in solving pattern problems efficiently that can not be addressed by using standard metric spaces. Our approach relies on a no... ...
An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operatorAbstract Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of thr... ...
Tập 2021 Số 1 - 2021
Convergence of proximal splitting algorithms in $\operatorname{CAT}(\kappa)$ spaces and beyondAbstract In the setting of$\operatorname{CAT}(\kappa)$ hiện toàn bộ
- 2021
Well-posedness analysis of a stationary Navier–Stokes hemivariational inequalityAbstract This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the tota... ...
- 2021
String-averaging methods for best approximation to common fixed point sets of operators: the finite and infinite casesAbstract String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm in hand requires to employ the operators in a specific order. Sequential orderings are well known, and a simultaneous order means that all operators are used simultaneously (in parallel). String-averaging allows to use strings of indices, ... ...
- 2021
Thuật toán ngưỡng thu nhỏ lặp cải tiến nhanh với sai số cho bài toán phục hồi hình ảnh Dịch bởi AI Tóm tắt Trong bài báo này, chúng tôi giới thiệu một phương pháp phân tách tiến-lùi lặp mới với sai số để giải quyết vấn đề bao gồm biến phân của tổng hai toán tử đơn điệu trong không gian Hilbert thực. Chúng tôi đề xuất và phân tích phương pháp này dưới một số điều kiện nhẹ nhàng thích hợp áp dụng cho các tham số, sao cho một định lý hội tụ mạnh khác cho những vấn đ... ...
- 2021
History-dependent operators and prox-regular sweeping processesAbstract We consider an abstract inclusion in a real Hilbert space, governed by an almost history-dependent operator and a time-dependent multimapping with prox-regular values. We establish the unique solvability of the inclusion under appropriate assumptions on the data. The proof is based on the arguments of monotonicity, fixed point, and prox-regularity. We then ... ...
- 2022
On a generalization of a relatively nonexpansive mapping and best proximity pairAbstract Let A and B be two nonempty subsets of a normed space X , and let $T: A \cup B \to A \cup B$
T
:
A
∪
B
→
A
∪
B
T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping $f: C \to C$ hiện toàn bộ
Tập 2023 Số 1
Random block-coordinate methods for inconsistent convex optimisation problems Abstract We develop a novel randomised block-coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying midway between the celebrated Chambolle–Pock primal-dual algorithm and Tseng’s accelerated proximal gradient method, we establish global convergence of the last iterate as well as optimal ...