Emergence of Self-Identity in Artificial Intelligence: A Mathematical Framework and Empirical Study with Generative Large Language Models by Minhyeok Lee

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A Version of the Hahn-Banach Theorem for R-Vector Spaces by Azadeh Alijani, Zohreh Heydarpour, Maryam Naderi Parizi

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Insights of window-bsed mechanism approach to visualize composite bioData point in feature spaces by Mosaab Daoud

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On coincidence and common fixed points of nearly densifying mappings by Zeqing Liu, Jeong Sheok Ume

Subjects: “…Complete metric space…”
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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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Coupled Fixed Point Theorems under Weak Contractions by Y. J. Cho, Z. Kadelburg, R. Saadati, W. Shatanawi

“…Appl. 61(2011), 1254–1260] studied common fixed point theorems on cone metric spaces by using the concept of c-distance. In this paper, we prove some coupled fixed point theorems in ordered cone metric spaces by using the concept of c-distance in cone metric spaces.…”
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Some Extensions of Fixed Point Results over Quasi-JS-Spaces by Maha Noorwali, Hamed H. Alsulami, Erdal Karapınar

“…We introduce the notion of quasi-JS-metric space. After defining the basic topological properties of quasi-JS-metric space, we investigate fixed point of certain mapping in the frame of complete quasi-JS-metric space. …”
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Common Fixed Points of Two Mappings regarding a Generalized c-Distance over a Banach Algebra by Ladan Aryanpour, Hamidreza Rahimi, Ghasem Soleimani Rad

“…Our results are interesting, since they are not equivalent to former well-known results regarding a wt-distance in b-metric spaces while they contain recent results corresponding to a generalized c-distance in cone b-metric spaces.…”
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Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications by Muhammad Aslam, Hassen Aydi, Samina Batul, Amna Naz

“…Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.…”
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Homotopy Characterization of ANR Function Spaces by Jaka Smrekar

“…Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. …”
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On Fixed-Point Results of Generalized Contractions by Shazia Kanwal, Umair Hanif, Maha Eshaq Noorwali, Md. Ashraful Alam

“…Our results generalize and extend several well-known results in metric and b-metric spaces.…”
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Fixed point theorems for densifying mappings and compact mappings by Zeqing Liu, Li Wang, Shin Min Kang, Yong Soo Kim

“…The purpose of this note is to establish fixed point theorems for densifying mappings and compact mappings which are contractive in metric spaces and to investigate the existence of fixed points for a family of mappings in bounded metric spaces. …”
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Common fixed point theorems and applications by Hemant Kumar Pathak, Shih Sen Chang, Yeol Je Cho, Jong Soo Jung

“…The purpose of this paper is to discuss the existence of common fixed points for mappings in general quasi-metric spaces. As applications, some common fixed point theorems for mappings in probabilistic quasi-metric spaces are given. …”
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On Topological Properties of Metrics Defined via Generalized “Linking Construction” by Marcin Borkowski, Dariusz Bugajewski, Adam Burchardt

“…We analyze topological properties of metric spaces obtained by using Száz’s construction, which we used to call generalized “linking construction.” …”
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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. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.…”
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Functional-Type Caristi–Kirk Theorem on Menger Space and Application by Soumia Chaira, Mohammed Dahmouni, Abderrahim Eladraoui, Mustapha Kabil

“…In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. …”
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Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces by Jiang Zhu, Lei Wei, Yeol Je Cho, Cheng Cheng Zhu

“…The results of this paper extend, generalize, and improve the corresponding results for Ekeland's variational principles of the directed vectorial perturbation type and other generalizations of Ekeland's variational principles in the setting of F-type topological space and quasi-metric spaces in the literatures. Even in usual real metric spaces, some of our results are new.…”
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Coupled and Tripled Coincidence Point Results with Application to Fredholm Integral Equations by Marwan Amin Kutbi, Nawab Hussain, Jamal Rezaei Roshan, Vahid Parvaneh

“…The aim of this paper is to define weak α-ψ-φ-contractive mappings and to establish coupled and tripled coincidence point theorems for such mappings defined on Gb-metric spaces using the concept of rectangular G-α-admissibility. …”
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Best Proximity Point Results for Modified --Proximal Rational Contractions by N. Hussain, M. A. Kutbi, P. Salimi

“…Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. …”
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On Pata Convex-Type Contractive Mappings by Merve Aktay, Murat Özdemir

“…In this work, we introduce weak Pata convex contractions and weak E-Pata convex contractions via simulation functions in metric spaces to prove some fixed point results for such mappings. …”
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