Transfinite methods in metric fixed-point theory by W. A. Kirk

“…Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.…”
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Approximation by q-Post-Widder Operators Based on a New Parameter by Qiu Lin

“…Weighted approximation and the quantitative q-Voronovskaja type theorem are discussed. Finally, numerical illustrative examples have been given to show the convergence of these newly defined operators.…”
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Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response by Runxin Wu, Lin Li

“…By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. …”
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Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition by Pavel A. Krutitskii

“…Thereby the existence theorem is proved. Besides, the uniqueness of the solution is studied. …”
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On a Predator-Prey Model Involving Age and Spatial Structure by Okana S. Sougué, Oumar Traoré

“…Using the fixed point theorem, we first show a global existence result for the problem with spatial variable. …”
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Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions by Guotao Wang, Sanyang Liu, Lihong Zhang

“…By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.…”
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Two Sufficient Conditions for Hamilton and Dominating Cycles by Zh. G. Nikoghosyan

“…The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. …”
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The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation by Qian Guo, Xueyin Tao

“…Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis.…”
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Viscosity Projection Algorithms for Pseudocontractive Mappings in Hilbert Spaces by Xiujuan Pan, Shin Min Kang, Young Chel Kwun

“…An explicit projection algorithm with viscosity technique is constructed for finding the fixed points of the pseudocontractive mapping in Hilbert spaces. Strong convergence theorem is demonstrated. Consequently, as an application, we can approximate to the minimum-norm fixed point of the pseudocontractive mapping.…”
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Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem by Tetsuo Inoue

“…Potentially theoretical schemes in the fundamental solutions method will be proposed for Dirichlet problems of unbounded and bounded Jordan domains. The asymptotic theorem on extremal weighted polynomials will play fundamental roles to introduce a new scheme and to determine the distribution of charge points. …”
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Strong Convergence for a Strongly Quasi-Nonexpansive Sequence in Hilbert Spaces by Satit Saejung, Kanokwan Wongchan

“…We prove a strong convergence theorem for strongly quasi-nonexpansive sequence of mappings in Hilbert spaces. …”
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A Generalization of Lacunary Equistatistical Convergence of Positive Linear Operators by Yusuf Kaya, Nazmiye Gönül

“…In this paper we consider some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence. …”
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On (𝑁,𝑝,𝑞)(𝐸,1) Summability of Fourier Series by H. K. Nigam, Ajay Sharma

“…A new theorem on (𝑁,𝑝,𝑞)(𝐸,1) summability of Fourier series has been established.…”
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Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials by Meihua Huang, Zhan Zhou

“…We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero.…”
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A nonlinear second order problem with a nonlocal boundary condition

“…Using an extension of Mawhin's continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman-Lazer type condition. …”
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On an initial-boundary value problem for the nonlinear Schrödinger equation by Herbert Gajewski

“…We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.…”
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Solving an Integral Equation via Orthogonal Branciari Metric Spaces by Aiman Mukheimer, Arul Joseph Gnanaprakasam, Absar Ul Haq, Senthil Kumar Prakasam, Gunaseelan Mani, Imran Abbas Baloch

“…In this article, we present an orthogonal L-contraction mapping concepts and prove a fixed point theorem on orthogonal complete Branciari metric spaces. …”
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Some Comments on Rigorous Finite-Volume Euclidean Quantum Field Path Integrals in the Analytical Regularization Scheme by Luiz C. L. Botelho

“…Through the systematic use of the Minlos theorem on the support of cylindrical measures on 𝑅∞, we produce several mathematically rigorous finite-volume euclidean path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of finite-volume Laplacian operator.…”
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Multiple Solutions for a Class of Multipoint Boundary Value Systems Driven by a One-Dimensional (𝑝1,…,𝑝𝑛)-Laplacian Operator by Shapour Heidarkhani

“…Employing a recent three critical points theorem due to Bonanno and Marano (2010), the existence of at least three solutions for the following multipoint boundary value system −(|𝑢𝑖|𝑝𝑖−2𝑢𝑖)′=𝜆𝐹𝑢𝑖(𝑥,𝑢1,…,𝑢𝑛) in (0,1), 𝑢𝑖∑(0)=𝑚𝑗=1𝑎𝑗𝑢𝑖(𝑥𝑗), 𝑢𝑖∑(1)=𝑚𝑗=1𝑏𝑗𝑢𝑖(𝑥𝑗) for 1≤𝑖≤𝑛, is established.…”
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Anticontrol of Chaos for a Class of Delay Difference Equations Based on Heteroclinic Cycles Connecting Repellers by Zongcheng Li

“…Then, a chaotification theorem based on the heteroclinic cycles connecting repellers for maps is established. …”
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