Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
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Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics by Lifang Guo, Salha Alshaikey, Abeer Alshejari, Muhammad Din, Umar Ishtiaq

“…Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result.…”
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Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative by Surendar Kumar Yadav, Mridula Purohit, Murli Manohar Gour, Lokesh Kumar Yadav, Manvendra Narayan Mishra

“…The proposed approach combines the Shehu transformation (ST) with the Adomian decomposition method (ADM), employing Adomain polynomials to handle nonlinear terms. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. …”
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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present to illustrate our main result.…”
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Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result by Noreddine Makran, Stojan N. Radenović

“…Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy b-metric spaces is investigated. …”
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Relational Almost (<i>ϕ</i>,<i>ψ</i>)-Contractions and Applications to Nonlinear Fredholm Integral Equations by Fahad M. Alamrani, Ebrahem A. Algehyne, Esmail Alshaban, Adel Alatawi, Hamid I. A. Mohammed, Faizan Ahmad Khan

“…In the course of the procedure, we also derive a related fixed point theorem for strict almost <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ϕ</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-contraction. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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Exponential Growth and Properties of Solutions for a Forced System of Incompressible Navier–Stokes Equations in Sobolev–Gevrey Spaces by José Luis Díaz Palencia

“…Utilizing the Banach fixed-point theorem, we demonstrate that the nonlinear operator associated with the Navier–Stokes equations is locally Lipschitz continuous in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>a</mi><mo>,</mo><mi>σ</mi></mrow><mn>1</mn></msubsup><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. …”
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Discrete Fractional-Order Modeling of Recurrent Childhood Diseases Using the Caputo Difference Operator by Yasir A. Madani, Zeeshan Ali, Mohammed Rabih, Amer Alsulami, Nidal H. E. Eljaneid, Khaled Aldwoah, Blgys Muflh

“…The existence theory is established using Brouwer’s fixed-point theorem and the Banach contraction principle, providing a comprehensive mathematical foundation for the model. …”
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A Proposal for Revisiting Ćirić and Caristi Type Theorems in Metric Spaces by Belkassem Seddoug, Soumia Chaira, Karim Chaira

“…In this paper, we revisit the renowned fixed point theorems of Ćirić and Caristi. We propose some new fixed point theorems in a metric space with partial order. …”
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The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with 𝑤-Distances by Hossein Lakzian, Ing-Jer Lin

“…Some fixed point theorems for (𝜑,𝜓,𝑝)-contractive maps and (𝜑,𝑘,𝑝)-contractive maps on a complete metric space are proved. …”
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Solution of Nonlinear Fredholm Integral Equations on Almost Z⊥-Contraction by Gunasekaran Nallaselli, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Khalil Javed, Yahya Almalki

“…In this manuscript, we develop an orthogonal to basically Z-contraction and demonstrate various fixed point theorems of nonlinear Fredholm integral equation solutions in such a contraction. …”
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Some Equivalences between Cone b-Metric Spaces and b-Metric Spaces by Poom Kumam, Nguyen Van Dung, Vo Thi Le Hang

“…As applications, we show that fixed point theorems on cone b-metric spaces can be obtained from fixed point theorems on b-metric spaces.…”
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Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions by S. Nageswara Rao, Ahmed Hussein Msmali, Manoj Singh, Abdullah Ali H. Ahmadini

“…Our results are based on some classical fixed point theorems such as Banach contraction mapping principle, Leray-Schauder fixed point theorems. …”
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On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings in D-metric spaces by B. C. Dhage, A. Jennifer Asha, S. M. Kang

“…Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000) and Rhoades (1996).…”
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A New Approach to Fixed Point Results in Triangular Intuitionistic Fuzzy Metric Spaces by N. Hussain, S. Khaleghizadeh, P. Salimi, Afrah A. N. Abdou

“…The aim of this paper is to propose some fixed point theorems in complete parametric metric spaces. …”
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An Application of Fixed Point Theory to a Nonlinear Differential Equation by A. P. Farajzadeh, A. Kaewcharoen, S. Plubtieng

“…We introduce a new family of mappings on [0,+∞) by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for α-ψ-contractive-type mappings in the setting of complete metric spaces. …”
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Fixed Point Theory in α-Complete Metric Spaces with Applications by N. Hussain, M. A. Kutbi, P. Salimi

“…As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for ψ-graphic-rational contractions. …”
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Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation by Mian Bahadur Zada, Muhammad Sarwar, Thabet Abdeljawad, Fahd Jarad

“…In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. …”
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Non-Expansive Multi-Valued Mappings and Convexity in Fuzzy Metric Space by Mohammad Rashid

“…Within these star-shaped subsets, we showcase various fixed point theorems for mappings of the non-expansive type that commute. …”
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