Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A by Dongjie Gao

“…We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.…”
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Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions by Qi Wang, Yanping Guo, Yude Ji

“…The associated Green's function for the fourth-order boundary value problems is first given, and the arguments are based on Krasnoselskii's fixed point theorem for operators on a cone.…”
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A Note on the Fixed Point of Generalized Eventual Cyclic Gross Contractive Mappings by Jin Liang, Sheng-Hua Yan

“…Furthermore, we analyze the existence of a fixed point for this type of contractive mapping, and present a new and general fixed point theorem.…”
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(α,ψ)-Meir-Keeler Contraction Mappings in Generalized b-Metric Spaces by Erdal Karapinar, Stefan Czerwik, Hassen Aydi

“…We present a fixed point theorem for generalized (α,ψ)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. …”
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Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces by Yulin Zhao, Li Huang, Xuebin Wang, Xianyang Zhu

“…By means of the fixed-point theorem in the cone of strict-set-contraction operators, we consider the existence of a nonlinear multi-point boundary value problem of fractional integro-differential equation in a Banach space. …”
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Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative by Ndolane Sene

“…The existence of α-resolvent operator in Banach space and fixed point theorem has been utilized in the proof of the existence of the mild solution. …”
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Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays by Lili Zhao, Yongkun Li

“…Some sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of weighted pseudo-almost periodic solutions to a class of neutral type high-order Hopfield neural networks with distributed delays by employing fixed point theorem and differential inequality techniques. …”
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Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of ℝn by Noureddine Zeddini

“…Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem.…”
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Remarks of Fixed Point for (ψ,φ)-Weakly Contractive Mappings by Zhiqun Xue, Guiwen Lv

“…In this paper, we obtain a new fixed point theorem for weak contraction mappings on complete generalized metric spaces. …”
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Positive Solutions for Singular p-Laplacian Fractional Differential System with Integral Boundary Conditions by Liping Wang, Zongfu Zhou, Hui Zhou

“…By using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions to the boundary value system is guaranteed.…”
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Application of Coupled Fixed Point Technique in Solving Integral Equations on Modified Intuitionistic Fuzzy Metric Spaces by Bhavana Deshpande, Amrish Handa

“…We establish a common coupled fixed point theorem for weakly compatible mappings on modified intuitionistic fuzzy metric spaces. …”
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On the Positive Almost Periodic Solutions of a Class of Nonlinear Lotka-Volterra Type System with Feedback Control by Ni Hua, Tian Li-Xin, Yao Hong-Xing

“…With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. …”
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Null controllability of a nonlinear population dynamics problem by Oumar Traore

“…Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, we show that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extinction.…”
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The Existence Results of Solutions for System of Fractional Differential Equations with Integral Boundary Conditions by Dongxia Zan, Run Xu

“…In this paper, we investigated the system of fractional differential equations with integral boundary conditions. By using a fixed point theorem in the Banach spaces, we get the existence of solutions for the fractional differential system. …”
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Positive Solutions for Third-Order Boundary Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives by Fei Yang, Yuanjian Lin, Juan Zhang, Quanfu Lou

“…In this paper, by the use of a new fixed point theorem and the Green function of BVPs, the existence of at least one positive solution for the third-order boundary value problem with the integral boundary conditions is considered,where there is a nonnegative continuous function. …”
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Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter by Yunhong Li, Weihua Jiang

“…On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. …”
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Travelling Waves of a Diffusive Epidemic Model with Latency and Relapse by Zhiping Wang, Rui Xu

“…The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder's fixed point theorem. Numerical simulations are carried out to illustrate the main results.…”
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Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings by R. K. Bisht

“…The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. …”
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The Stability of a General Sextic Functional Equation by Fixed Point Theory by Jaiok Roh, Yang-Hi Lee, Soon-Mo Jung

“…And by applying the fixed point theorem in the sense of Ca˘dariu and Radu, we will discuss the stability of the solutions for this functional equation.…”
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Existence Results for Fractional Differential Equations with Multistrip Riemann–Stieltjes Integral Boundary Conditions by Tongling Lv, Huihui Pang, Limei Cao

“…Our results are based on the Leggett–Williams fixed point theorem. In the end, two examples are worked out to illustrate our main work.…”
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