Transfinite methods in metric fixed-point theory by W. A. Kirk

“…This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. …”
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Variational Analysis, Optimization, and Fixed Point Theory by Qamrul Hasan Ansari, Mohamed Amine Khamsi, Abdul Latif, Jen-Chih Yao

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The Fixed Point Theory for Some Generalized Nonexpansive Mappings by Enrique Llorens Fuster, Elena Moreno Gálvez

“…We study some aspects of the fixed point theory for a class of generalized nonexpansive mappings, which among others contain the class of generalized nonexpansive mappings recently defined by Suzuki in 2008.…”
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Solving Integral Equations by Means of Fixed Point Theory by E. Karapinar, A. Fulga, N. Shahzad, A. F. Roldán López de Hierro

“…One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. …”
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On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory by Areej S. S. Alharbi, Hamed H. Alsulami, Erdal Karapinar

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An Application of Fixed Point Theory to a Nonlinear Differential Equation by A. P. Farajzadeh, A. Kaewcharoen, S. Plubtieng

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Fixed Point Theory in α-Complete Metric Spaces with Applications by N. Hussain, M. A. Kutbi, P. Salimi

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A Note on tvs-G-Cone Metric Fixed Point Theory by Ing-Jer Lin, Chi-Ming Chen, Chao-Hung Chen, Tien-Ying Cheng

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The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps by Wei-Shih Du, Erdal Karapınar, Naseer Shahzad

“…The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.…”
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Ulam-Hyers Stability for MKC Mappings via Fixed Point Theory by Anisa Mukhtar Hassan, Erdal Karapınar, Hamed H. Alsulami

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The Stability of a General Sextic Functional Equation by Fixed Point Theory by Jaiok Roh, Yang-Hi Lee, Soon-Mo Jung

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Nonlinear Operators in Fixed Point Theory with Applications to Fractional Differential and Integral Equations by Jamshaid Ahmad, Ahmad Saleh Al-Rawashdeh, Talat Nazir, Vahid Parvaneh, Manuel De la Sen

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The Fixed Point Theory and the Existence of the Periodic Solution on a Nonlinear Differential Equation by Ni Hua

“…This paper deals with a nonlinear differential equation, by using the fixed point theory. The existence of the periodic solution of the nonlinear differential equation is obtained; these results are new.…”
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Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms by Shahram Rezapour, Ali Boulfoul, Brahim Tellab, Mohammad Esmael Samei, Sina Etemad, Reny George

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Ordered Uniform Convexity in Ordered Convex Metric Spaces with an Application to Fixed Point Theory by Ismat Beg

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A New Approach for the Approximations of Solutions to a Common Fixed Point Problem in Metric Fixed Point Theory by Ishak Altun, Nassir Al Arifi, Mohamed Jleli, Aref Lashin, Bessem Samet

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Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory by Ruofeng Rao, Shouming Zhong

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Equivalent Cauchy Sequences in q1,q2-Quasi Metric-Like Space and Applications to Fixed-Point Theory by Eriola Sila, Sidite Duraj, Elida Hoxha

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Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives by Said Zibar, Brahim Tellab, Abdelkader Amara, Homan Emadifar, Atul Kumar, Sabir Widatalla

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Remarks on Some Results of Extended Interpolative Hardy-Rogers-Geraghty-Wardowski Contractions and Ćirić-Reich-Rus Type F-Contractions by Dušan Bajović, Slobodanka Mitrović, Sandra Buhmiler, Stojan Radenovic

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