On coincidence theorems for a family of mappings in convex metric spaces by Olga Hadzic

“…This theorem is a generalization of the well known fixed point theorem proved by Assad and Kirk. As an application a common fixed point theorem in metric spaces with a convex structure is obtained.…”
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Fractional Differential Equations with Fractional Impulsive and Nonseparated Boundary Conditions by Xi Fu, Xiaoyou Liu

“…By means of Schaefer fixed point theorem, Banach fixed point theorem, and nonlinear alternative of Leray-Schauder type, some existence results are obtained. …”
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Existence Results of Random Impulsive Integrodifferential Inclusions with Time-Varying Delays by Sahar M. A. Maqbol, R. S. Jain, B. S. Reddy

“…Our study is based on the Martelli fixed point theorem, Pachpatte’s inequality, and the fixed point theorem due to Covitz and Nadler. …”
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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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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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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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Fractional Langevin Equations with Nonseparated Integral Boundary Conditions by Khalid Hilal, Lahcen Ibnelazyz, Karim Guida, Said Melliani

“…In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. …”
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation by Jing Li, Yuhai Zhang

“…The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1≤δi<0 is investigated. A fixed point theorem in partially ordered sets is proved. …”
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The Existence of Cone Critical Point and Common Fixed Point with Applications by Wei-Shih Du

“…We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. …”
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Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations by Ping Yu, Hongju Li, Jian Ding, Yanli Ma

“…The proof of the main result is based on Gatica–Oliker–Waltman fixed-point theorem. At last, an example is given to illustrate our main conclusion.…”
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A Study on ψ-Caputo-Type Hybrid Multifractional Differential Equations with Hybrid Boundary Conditions by Fouad Fredj, Hadda Hammouche, Mohammed S. Abdo, Wedad Albalawi, Abdulrazak H. Almaliki

“…Using an advantageous generalization of Krasnoselskii’s fixed point theorem, we establish results of at least one solution, whereas the uniqueness of solution is derived via Banach’s fixed point theorem. …”
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Fixed points of a certain class of mappings in spaces with uniformly normal structure by Jong Soo Jung, Balwant Singh Thakur, Daya Ram Sahu

“…This result generalizes a fixed point theorem of Górnicki [1].…”
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Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions by Jessada Tariboon, Sotiris K. Ntouyas, Chatthai Thaiprayoon

“…We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. …”
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Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales by Xue Xu, Yong Wang

“…The existence and uniqueness of positive solutions are established by using the mixed monotone fixed point theorem on cone and Krasnosel’skii fixed point theorem. …”
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Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations by Ruofeng Rao, Shouming Zhong

“…As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for T-S fuzzy CGNNs, and this inspires our present work. …”
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Three-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Equations Involving Different Numbers of q by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative) and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. …”
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Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions by Mısır J. Mardanov, Yagub A. Sharifov, Kamala E. Ismayilova

“…Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. …”
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Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations by Mohamed Hannabou, Hilal Khalid

“…We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for existence results. …”
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