Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions by Hui Li, Libo Wang, Minghe Pei

“…We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. …”
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Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. C. Serrano Pérez

“…The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.…”
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Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model by Ali Khalouta

“…We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition method ($\mathbb{J}$-DM) which is a combined form of the $\mathbb{J}$-transform method and a new decomposition method to solve the proposed model. …”
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Positive Periodic Solutions of a Periodic Discrete Competitive System Subject to Feedback Controls by Ronghua Tan, Zuxiong Li, Qinglong Wang, Zhijun Liu

“…By using the methods of discrete inequality, fixed point theorem, and analysis techniques, a good understanding of the existence and global asymptotic stability of positive periodic solutions is obtained. …”
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On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term by Binh Duy Ho, Van Kim Ho Thi, Long Le Dinh, Nguyen Hoang Luc, Phuong Nguyen

“…Our main idea is to combine theories of Banach’s fixed point theorem, Hilbert scale theory of space, and some Sobolev embedding.…”
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Recent Fixed-Point Results for θ−Contraction Mappings in Rectangular M−Metric Spaces with Supportive Application by Mustafa Mudhesh, Hasanen A. Hammad, Habes Alsamir, Muhammad Arshad, Eskandar Ameer

“…The goal of this manuscript is to present a new fixed-point theorem on θ−contraction mappings in the setting of rectangular M-metric spaces (RMMSs). …”
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Existence Theory for q-Antiperiodic Boundary Value Problems of Sequential q-Fractional Integrodifferential Equations by Ravi P. Agarwal, Bashir Ahmad, Ahmed Alsaedi, Hana Al-Hutami

“…Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. …”
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Multiple Solutions to Fractional Difference Boundary Value Problems by Huiqin Chen, Yaqiong Cui, Xianglan Zhao

“…Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on f which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. …”
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A System of Generalized Variational-Hemivariational Inequalities with Set-Valued Mappings by Zhi-bin Liu, Jian-hong Gou, Yi-bin Xiao, Xue-song Li

“…By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. …”
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Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse by Zhenguo Luo, Liping Luo, Yunhui Zeng

“…By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t)=x(t)[a(t)-f(t,x(t),x(t-τ1(t,x(t))),…,x(t-τn(t,x(t))),x'(t-γ1(t,x(t))),…,x'(t-γm(t,x(t))))],  t≠tk,  k∈Z+;  x(tk+)=x(tk-)+θk(x(tk)),  k∈Z+. …”
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Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions by Zhi-Xian Yu, Rong Yuan, Cheng-Hsiung Hsu, Ming-Shu Peng

“…Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.…”
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On Some Fixed Point Results in E−Fuzzy Metric Spaces by Rachid Mecheraoui, Zoran D. Mitrović, Vahid Parvaneh, Hassen Aydi, Naeem Saleem

“…In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. …”
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Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ-Hilfer Fractional Derivatives by Athasit Wongcharoen, Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Jessada Tariboon

“…We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. …”
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New Existence Results for Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Khalid Hilal, Said Melliani

“…In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative examples are studied to support the results.…”
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Some Modified Fixed Point Results in V-Fuzzy Metric Spaces by Vishal Gupta, Manu Verma, Mohammad Saeed Khan

“…The introduction of notion for pair of mappings (f,g) on V-fuzzy metric space called V-weakly commuting of type Vf and V-R weakly commuting of type Vf is given. This proved fixed point theorem in V-fuzzy metric space employing the effectiveness of E.A. property and CLRg property. …”
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Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales by Fuyi Xu

“…We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.…”
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Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control by Lingling Zhang, Noriaki Yamazaki, Rui Guo

“…Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. …”
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument by Kuo-Shou Chiu

“…Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. …”
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Existence and optimal control of Hilfer fractional evolution equations by Zhou Mian, Zhou Yong, He Jia Wei, Liang Yong

“…The first part focuses on analyzing the existence and uniqueness of the mild solution using the fixed point theorem and semigroup theory. In the second part, an optimal control problem that admits an optimal pair is considered. …”
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On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme by Satit Saejung

“…Lett. 24:308–313, 2011), utilizing Banach’s fixed point theorem. This result remains valid under weaker assumptions through the product space approach. …”
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