On common fixed points of weakly commuting mappings and set-valued mappings by S. Sessa, B. Fisher

“…This improves a theorem of the second author.…”
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Unicity of Entire Functions concerning Shifts and Difference Operators by Dan Liu, Degui Yang, Mingliang Fang

“…We prove a unicity theorem of entire functions that share two distinct small functions with their shifts. …”
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On Abstract Economies and Their Applications by Chien-Hao Huang, Liang-Ju Chu

“…We establish a new equilibrium existence theorem of generalized abstract economies with general preference correspondences. …”
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Existence Results for Fractional Differential Equations with Separated Boundary Conditions and Fractional Impulsive Conditions by Xi Fu, Xiaoyou Liu

“…By means of the Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. …”
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Approximation of the Summation-Integral-Type q-Szász-Mirakjan Operators by Mei-Ying Ren, Xiao-Ming Zeng

“…We establish local approximation theorem. We give weighted approximation theorem. Also we estimate the rate of convergence of these operators for functions of polynomial growth on the interval [0,∞).…”
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Kaplansky's ternary quadratic form by James Kelley

“…The proof is modelled on that of a similar theorem by Ono and Soundararajan, in which relations between the number of representations of an integer np2 by two quadratic forms in the same genus, the pth coefficient of an L-function of a suitable elliptic curve, and the class number formula prove the theorem for large primes, leaving 3 cases which are easily numerically verified.…”
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Existence and Multiplicity of Nontrivial Solutions for a Class of Fourth-Order Elliptic Equations by Chun Li, Zeng-Qi Ou, Chun-Lei Tang

“…Using the Fountain theorem and a version of the Local Linking theorem, we obtain some existence and multiplicity results for a class of fourth-order elliptic equations.…”
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Description of the structure of singular spectrum for Friedrichs model operator near singular point by Serguei I. Iakovlev

“…We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular spectrum.…”
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Eigen Solution of Neural Networks and Its Application in Prediction and Analysis of Controller Parameters of Grinding Robot in Complex Environments by Shixi Tang, Jinan Gu, Keming Tang, Wei Ding, Zhengyang Shang

“…Secondly, an eigen solution theory of general neural networks was proposed and proven including consistent approximation theorem, eigen solution existence theorem, consistency theorem of complete solution, the partial solution, and none solution theorem of neural networks. …”
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On Harmonic Functions Defined by Differential Operator with Respect to k-Symmetric Points by Afaf A. Ali Abubaker, Maslina Darus

“…We determine a sufficient coefficient condition, representation theorem, and distortion theorem.…”
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Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order by Yang Liu, Zhang Weiguo

“…The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.…”
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Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces by Lijie Li

“…Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. …”
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Ideal extensions of ordered sets by Niovi Kehayopulu

“…In this paper, we give the main theorem of the ideal extensions for ordered sets. …”
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Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations by Rongbo Wang, Qiang Feng

“…In this paper, fractional mixed-weighted convolution is defined based on the fractional cosine transform; the corresponding convolution theorem is achieved. The properties of fractional mixed-weighted convolution and Young’s type theorem are also explored. …”
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Permanence for a Discrete Model with Feedback Control and Delay by Yong-Hong Fan, Lin-Lin Wang

“…We found that if we use the method of comparison theorem, then the additional condition, to some extent, is necessary. …”
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Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials by Defang Ma, Zhan Zhou

“…New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved.…”
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A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions by Hamid Lmou, Khalid Hilal, Ahmed Kajouni

“…The existence and uniqueness results are obtained by making use of the Krasnoselskii fixed-point theorem and Banach contraction principle, and for the inclusion version, we use the Martelli fixed-point theorem to get the existence result. …”
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Fixed Points of Nonlinear and Asymptotic Contractions in the Modular Space by A. Razani, E. Nabizadeh, M. Beyg Mohamadi, S. Homaei Pour

“…A fixed point theorem for nonlinear contraction in the modular space is proved. …”
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Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures by Ting Xie, Zengtai Gong

“…Furthermore, the characterization theorem and transformation theorem for the integral are given. …”
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Cryptographic Censorship by Netta Engelhardt, Åsmund Folkestad, Adam Levine, Evita Verheijden, Lisa Yang

“…This result provides a general condition that guarantees (in finite time) event horizon formation, with minimal assumptions about the global spacetime structure. Our theorem relies on an extension of a recent quantum learning no-go theorem and is proved using new techniques of pseudorandom measure concentration. …”
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