Strong Convergence Theorems for Solutions of Equilibrium Problems and Common Fixed Points of a Finite Family of Asymptotically Nonextensive Nonself Mappings by Lijuan Zhang, Hui Tong, Ying Liu

“…An iterative algorithm for finding a common element of the set of common fixed points of a finite family of asymptotically nonextensive nonself mappings and the set of solutions for equilibrium problems is discussed. …”
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A Weak Convergence Theorem for Common Fixed Points of Two Nonlinear Mappings in Hilbert Spaces by Takanori Ibaraki, Shunsuke Kajiba, Yukio Takeuchi

“…In this paper, by using properties of attractive points, we study an iteration scheme combining simplified Baillon type and Mann type to find a common fixed point of commutative two nonlinear mappings in Hilbert spaces. …”
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Strong Convergence Theorems for Solutions of Equations of Hammerstein Type by Chih-Sheng Chuang

“…., monotone and bounded mappings). We use an explicit iterative process that converges strongly to a solution of equation of Hammerstein type. …”
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Construction of Compactly Supported Refinable Componentwise Polynomial Functions in ℝ2 by Yanmei Xue, Ning Bi

“…We provide a sufficient condition for constructing a class of compactly supported refinable functions with componentwise polynomial property in ℝ2. An iteration algorithm is developed to compute the polynomial on each component of the functions' support. …”
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Periodic and Antiperiodic Solutions for a Second-Order Hamiltonian System With Nonlinearity Depending on Derivative by Wenxiong Chen, Shibo Liu

“…We prove that there exists T0>0 such that, for any T<T0, the provided Hamiltonian system has a nontrivial T-periodic and T/2-antiperiodic solution via linking theorem and iteration method.…”
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Strong Convergence Theorems for the Generalized Split Common Fixed Point Problem by Cuijie Zhang

“…Moreover, we introduce a new iterative algorithm for finding a solution of the GSCFPP and obtain some strong convergence theorems under suitable assumptions.…”
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Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces by H. Zegeye, N. Shahzad

“…We introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. …”
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Regularity of Global Attractor for the Reaction-Diffusion Equation by Hong Luo

“…By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.…”
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An Inversion-Free Method for Finding Positive Definite Solution of a Rational Matrix Equation by Fazlollah Soleymani, Mahdi Sharifi, Solat Karimi Vanani, Farhad Khaksar Haghani, Adem Kılıçman

“…A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X+A*X-1A=I. …”
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Fixed Points and Stability for Integral-Type Multivalued Contractive Mappings by Zhefu An, Mengyao Li, Liangshi Zhao

“…The existence and iterative approximations of fixed points concerning two classes of integral-type multivalued contractive mappings in complete metric spaces are proved, and the stability of fixed point sets relative to these multivalued contractive mappings is established. …”
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Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces by Aihong Wang

“…We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of the solutions of the equilibrium problem and the set of fixed points of infinitely strict pseudocontractive mappings. …”
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Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications by Zi-Ming Wang, Poom Kumam

“…Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. …”
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A Continuous Trust-Region-Type Method for Solving Nonlinear Semidefinite Complementarity Problem by Ying Ji, Tienan Wang, Yijun Li

“…We propose a new method to solve nonlinear semidefinite complementarity problem by combining a continuous method and a trust-region-type method. At every iteration, we need to calculate a second-order cone subproblem. …”
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ON INEXACT TIKHONOV AND PROXIMAL POINT REGULARISATION METHODS FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS by Phạm Gia Hưng, Lê Dũng Mưu

“…In this ease, the regularised sub-problems may be not strongly monotone, even not pseudomonotone. However, any iterative sequence of the regularised sub-problems tends to the same solution of the original problem which is nearest to the starting point for the Tikhonov method.…”
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Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces by Meng Wen, Changsong Hu, Zhiyu Wu

“…We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. …”
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Some Convergence Theorems for Contractive Type Mappings in CAT(0) Spaces by Kyung Soo Kim

“…We establish theorems of strong convergence, for the Ishikawa-type (or two step; cf. Ishikawa, 1974) iteration scheme, to a fixed point of a uniformly L-Lipschitzian asymptotically demicontractive mapping and a uniformly L-Lipschitzian hemicontractive mapping in CAT(0) space. …”
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The local limit theorem for complex valued sequences: the parabolic case by Coulombel, Jean-François, Faye, Grégory

“…We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. …”
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Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems by Hamisu Musa, Buhari Alhassan

“…The SEBDF schemes are implemented using a Modified Newton iteration algorithm iterated to convergence in which some selected systems of first-order stiff IVPs are solved, and the numerical results obtained for the proposed methods are often better than the existing BDF and SBDF methods for solving stiff IVPs.…”
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CAREA: Cotraining Attribute and Relation Embeddings for Cross-Lingual Entity Alignment in Knowledge Graphs by Baiyang Chen, Xiaoliang Chen, Peng Lu, Yajun Du

“…This paper sets out to investigate cross-lingual entity alignment and proposes an iterative cotraining approach (CAREA) to train a pair of independent models. …”
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Gradient Method with Step Adaptation by Vladimir Krutikov, Elena Tovbis, Svetlana Gutova, Ivan Rozhnov, Lev Kazakovtsev

“…Such methods require only the gradient of the function to be calculated at the iteration. Optimization of the parameters of the step adaptation algorithms enables us to obtain methods that significantly exceed the steepest descent method in terms of convergence rate. …”
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