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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Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function by Bing-Wei Niu, Jian-Ping Sun, Qiu-Yan Ren

“…Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.…”
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Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters by Zhenguo Luo

“…By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of  n-dimension periodic impulsive functional differential equations with multiple delays and two parameters: xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+, and xi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e., t>0, t≠tk, k∈Z+, xi(tk+)-xi(tk-)=μcikxi(tk), i=1,2,…,n, k∈Z+. …”
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The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions by Wenjie Ma, Yujun Cui

“…By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.…”
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Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. …”
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Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales by Jian Liu, Fuyi Xu

“…We obtain the existence of three 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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Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces by Ravi P. Agarwal, Hamed H. Alsulami, Erdal Karapınar, Farshid Khojasteh

“…Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. …”
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Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications by Muhammad Aslam, Hassen Aydi, Samina Batul, Amna Naz

“…Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. …”
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Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions by Jian Chang, Jian-Ping Sun, Ya-Hong Zhao

“…Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. …”
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Existence of Bounded Positive Solutions for Partial Difference Equations with Delays by Zeqing Liu, Zhihua Wu, Young Chel Kwun, Shin Min Kang

“…With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the partial difference equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. …”
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Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order by J. Caballero, J. Harjani, K. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.…”
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Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian by Imed Bachar, Habib Mâagli, Said Mesloub

“…Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.…”
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Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems by S. Nageswara Rao, M. Zico Meetei

“…Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.…”
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Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian by Yanping Guo, Wenying Wei, Yuerong Chen

“…We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0, t∈{1,…,n−1} subject to the boundary conditions: u(0)=0, u(n)=∑i=1m−2aiu(ξi), where ϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2} with 1<ξ1<⋯<ξm−2<n−1 and ai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.…”
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Positive Solutions for Some Competitive Fractional Systems in Bounded Domains by Imed Bachar, Habib Mâagli, Noureddine Zeddini

“…Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. …”
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