Article
Mathematics
Shih-sen Chang, Lin Wang, Y. H. Zhao, G. Wang, Z. L. Ma
Summary: This paper investigates the split common fixed point problem for quasi-pseudo-contractive mappings in Hilbert spaces, proposing a new algorithm and strong convergence theorems under appropriate assumptions. The results not only enhance and extend previous findings, but also provide a positive answer to an open question.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics
Yuanheng Wang, Tiantian Xu, Jen-Chih Yao, Bingnan Jiang
Summary: This paper proposes a new method to solve the split feasibility problem and the fixed-point problem involving quasi-nonexpansive mappings. By relaxing the conditions of the operator and considering the inertial iteration and adaptive step size, our algorithm achieves better convergence and faster convergence rate compared to previous algorithms.
Article
Mathematics
Konrawut Khammahawong, Parin Chaipunya, Kamonrat Sombut
Summary: The aim of this research is to propose a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds, and discuss the convergence theorem of the proposed method under certain conditions. Numerical examples are provided to support the results for clarity. Furthermore, the suggested approach is applied to solve inclusion problems and convex feasibility problems.
Article
Mathematics, Applied
Hammed Anuoluwapo Abass, Lateef Olakunle Jolaoso
Summary: The paper proposes a generalized viscosity iterative algorithm for solving multiple-set split feasibility problems and fixed point problems, with the advantage of a self adaptive step size. Strong convergence results are proven for the algorithm, and numerical examples are presented to demonstrate its efficiency and accuracy. The results presented extend and complement recent findings in the literature.
Article
Mathematics, Applied
Jing Zhao, Yuan Li
Summary: This paper studies the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space and establishes a weak convergence theorem for the proposed iterative algorithm, which combines the primal-dual method and the inertial method. The algorithm adapts step sizes self-adaptively, eliminating the need for prior information about bounded linear operator norms. Numerical results demonstrate the efficiency of the proposed algorithm.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics
Fugen Gao, Xiaoxiao Liu, Xiaochun Li
Summary: This paper introduces a new iterative algorithm for solving the split feasibility problem in real Hilbert space with nonempty, closed, and convex sets, by combining W-mapping with viscosity. It is proven that the proposed algorithm strongly converges to a solution of the split feasibility problem.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Lulu Li, Hong-Kun Xu
Summary: The study focused on convergence analysis of iterative algorithms proposed in [33] for the generalized split feasibility problem, obtaining weak convergence results under more relaxed conditions. Regularization was introduced to achieve strong convergence of the viscosity approximation method.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Mathematics, Applied
A. Taiwo, L. O. Jolaoso, O. T. Mewomo
Summary: This paper explores the properties of firmly nonexpansive-like mappings in Banach spaces and proposes an inertial-type shrinking projection algorithm for solving split common fixed point problems, proving its strong convergence. The results complement previous research in this area and represent a novel use of inertial techniques outside of Hilbert spaces.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics
Hammed A. Abass, Olawale K. Oyewole, Akindele A. Mebawondu, Kazeem O. Aremu, Ojen K. Narain
Summary: This paper introduces a hybrid extragradient iterative algorithm based on the works of several scholars. The algorithm utilizes the Bregman distance approach to approximate a common solution to split feasibility problems and fixed point problems. The convergence of the proposed method is demonstrated through a numerical example.
DEMONSTRATIO MATHEMATICA
(2022)
Article
Mathematics, Applied
Shuja H. Rizvi, Fahad Sikander
Summary: The aim of this study is to investigate an iterative method to find a common solution of a split equilibrium problem, split variational inequality problem and fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Strong convergence theorem is obtained under mild conditions, and some special cases of the main result are included. Numerical experiments are provided to justify the main result, which can be considered as an improvement, extension, and refinement of some corresponding results in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Operations Research & Management Science
Mohammad Eslannian
Summary: In this paper, we study the split common fixed point problem for a finite family of demimetric mappings and a finite family of Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem of Halpern's type iteration for finding a solution of the split common fixed point problem.
Article
Mathematics, Applied
Charles E. Chidume, Abubakar Adamu
Summary: A new iterative algorithm is proposed and studied for approximating a solution of a split feasibility problem and the fixed point problem of a quasi-phi-nonexpansive mapping. It is proved that the sequence generated by the algorithm converges strongly to a common solution of the split feasibility problem and the fixed point problem in real Banach spaces, which are more general than Hilbert spaces.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Shaotao Hu, Yuanheng Wang, Liya Liu, Qiao-Li Dong
Summary: In this paper, a new self adaptive iterative algorithm with an inertial technique is proposed to solve split feasibility problems and fixed point problems. The algorithm is applicable in p-uniformly convex and uniformly smooth Banach spaces. It is proven that the algorithm converges strongly to a common solution of the mentioned problems, under appropriate assumptions on the parameters and operators. The algorithm does not require prior knowledge of the norm of the bounded linear operator as it utilizes a new self adaptive step size. Numerical examples are provided to demonstrate the effectiveness and feasibility of the algorithm.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Chadarat Thongphaen, Warunun Inthakon, Suthep Suantai, Narawadee Phudolsitthiphat
Summary: In this work, the basic properties of the set of common attractive points are studied, and strong convergence results are proven for common attractive points of two generalized nonexpansive mappings in a uniformly convex Banach space. As a result, a common fixed point result of such mappings is obtained and applied to solve the convex minimization problem. Finally, numerical experiments are provided to support the results.
Article
Mathematics, Applied
Suliman Al-Homidan, Bashir Ali, Yusuf Suleiman
Summary: This paper investigates the generalized split feasibility problem (GSFP) in p uniformly convex Banach spaces, highlighting some special cases and proving a self adaptive step-size iterative algorithm which strongly converges to the solution of GSFP. The method is demonstrated with two numerical examples and does not require prior information of operator norms. The results extend, improve and enrich previously announced related results in the literature.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Genaro Lopez, Victoria Martin-Marquez, Fenghui Wang, Hong-Kun Xu
Article
Operations Research & Management Science
Fenghui Wang
JOURNAL OF GLOBAL OPTIMIZATION
(2011)
Article
Mathematics, Applied
Fenghui Wang, Bijun Pang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2009)
Article
Mathematics
Fenghui Wang, Changsen Yang
STUDIA MATHEMATICA
(2010)
Article
Mathematics, Applied
Fenghui Wang
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2007)
Article
Mathematics, Applied
Guglielmo Feltrin, Maurizio Garrione
Summary: This article deals with a non-autonomous parameter-dependent second-order differential equation driven by a Minkowski-curvature operator. It proves the existence of strictly increasing heteroclinic solutions and homoclinic solutions with a unique change of monotonicity under suitable assumptions, and analyzes the asymptotic behavior of these solutions.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Mehraj Ahmad Lone, Idrees Fayaz Harry
Summary: In this paper, we study Lorentzian generalized Sasakian space forms admitting Ricci soliton, conformal gradient Ricci soliton, and Ricci Yamabe soliton. We also investigate the conditions for solitons to be steady, shrinking, and expanding. Additionally, we provide applications of Ricci Yamabe solitons.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhihao Lu
Summary: We present a unified method for deriving differential Harnack inequalities for positive solutions to semilinear parabolic equations, subject to an integral curvature condition, on compact manifolds and complete Riemannian manifolds. In addition to the case of scalar equations, we also establish an elliptic estimate for the heat flow under the same condition, which is a novel result for both harmonic map and heat equations.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giuseppe Cosma Brusca
Summary: We investigate the asymptotic behavior of the minimal heterogeneous d-capacity of a small set in a fixed bounded open set Omega. We prove that this capacity is related to the parameter lambda and behaves as C |log epsilon|^(1-d), where C is a constant.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Stefan Schiffer
Summary: This note investigates the complex constant rank condition for differential operators and its implications for coercive differential inequalities. Depending on the order of the operators, such inequalities can be viewed as generalizations of either Korn's inequality or Sobolev's inequality.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Konstantinos T. Gkikas, Phuoc-Tai Nguyen
Summary: This article studies the boundary value problem with an inverse-square potential and measure data. By analyzing the Green kernel and Martin kernel and using appropriate capacities, necessary and sufficient conditions for the existence of a solution are established in different cases.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Giovanni Bellettini, Simone Carano, Riccardo Scala
Summary: This article computes the relaxed Cartesian area in the strict BV-convergence for a class of piecewise Lipschitz maps from the plane to the plane, where the jump is composed of multiple curves that are allowed to meet at a finite number of junction points. It is shown that the domain of this relaxed area is strictly contained within the domain of the classical L1-relaxed area.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, Jeremy Sok
Summary: In this paper, we establish the well-posedness of a perturbed Dirac equation with a moving potential W satisfying the Klein-Gordon equation. This serves as a toy model for atoms with relativistic corrections, where the wave function of electrons interacts with an electric field generated by a nucleus with a given charge density. A key contribution of this paper is the development of a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation, which is of independent interest.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Jingwen Chen
Summary: In this article, the authors generalize their previous results to higher dimensions and prove the existence of eternal weak mean root 1 root-1 curvature flows connecting a Clifford hypersurface to the equatorial spheres.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Samuel Borza, Wilhelm Klingenberg
Summary: This article proves that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points, and characterizes conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Christina Sormani, Wenchuan Tian, Changliang Wang
Summary: This article presents a sequence of warped product manifolds that satisfy certain hypotheses and proves that this sequence converges in a weak sense to a limit space with nonnegative scalar curvature.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gianni Dal Maso, Davide Donati
Summary: In this paper, we study the F-limits of sequences of quadratic functionals and bounded linear functionals on the Sobolev space, and show that their limits can always be expressed as the sum of a quadratic functional, a linear functional, and a non-positive constant. Furthermore, we prove that the coefficients of the quadratic and linear parts in the Gamma-limit are independent of Omega, and introduce an example to demonstrate that the previous results cannot be generalized to every bounded open set.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Laura Abatangelo, Corentin Lena, Paolo Musolino
Summary: The paper provides a full series expansion of a generalization of the u-capacity related to the Dirichlet-Laplacian in dimension three and higher. The results extend the previous findings on the planar case and are applied to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Gustavo de Paula Ramos
Summary: This paper employs the photography method to estimate the number of solutions to a nonlinear elliptic problem on a Riemannian orbifold, based on the Lusternik-Schnirelmann category of its submanifold of points with the largest local group.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Mathematics, Applied
Tim Espin, Aram Karakhanyan
Summary: This article discusses smooth solutions of the Monge-Ampere equation on an annular domain with two smooth, closed, strictly convex hypersurfaces as boundaries, subject to mixed boundary conditions. It is demonstrated that global C2 estimates cannot be obtained in general unless additional restrictions are imposed on the principal curvatures of the inner boundary and the Neumann condition itself, as shown by an explicit counterexample. Under these conditions, a priori C2 estimates are proven and it is shown that the problem has a smooth solution.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)