Penot’s Compactness Property in Ultrametric Spaces with an Application by Mostafa Bachar, Messaoud Bounkhel, Samih Lazaiz

“…The spherical completeness property misled some mathematicians to it to hyperconvexity in metric spaces. As an application, we discuss some fixed point results in spherically complete ultrametric spaces.…”
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On Some Common Fixed Point Results for Weakly Contraction Mappings with Application by Yan Hao, Hongyan Guan

“…In this paper, we introduce a new class of generalized weakly contractive mappings and prove common fixed point results by using different algorithms involving this new class of mappings in the framework of b-metric spaces, which generalize the results of Cho. We also provide two examples to show the applicability and validity of our results. …”
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Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings by Marin Borcut, Mădălina Păcurar, Vasile Berinde

“…We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. …”
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Some Fixed Point Theorems for Nonlinear Set-Valued Contractive Mappings by Zeqing Liu, Zhihua Wu, Shin Min Kang, Sunhong Lee

“…Four fixed point theorems for nonlinear set-valued contractive mappings in complete metric spaces are proved. The results presented in this paper are extensions of a few well-known fixed point theorems. …”
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The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications by Marwan Amin Kutbi, Wutiphol Sintunavarat

“…We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. …”
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Common fixed point theorems for nonself-mappings in metrically convex spaces via altering distances by M. Imdad, Ladlay Khan

“…Some common fixed point theorems for a pair of nonself-mappings in complete metrically convex metric spaces are proved by alte ring distances between the points, which generalize earlier results due to M. …”
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On Some New Fixed Point Results with Applications to Matrix Difference Equations by Marwan Amin Kutbi, Jamshaid Ahmad, Muhammad Imran Shahzad

“…The aim of this article is to discuss the convergence of iterative sequences of the Prešić type involving new classes of operators satisfying Prešić type Θ-contractive condition in the context of metric spaces. Some examples are also provided to show the significance of the investigation of finding fixed points. …”
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New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness by Wei-Shih Du

“…Some new existence theorems concerning approximate coincidence point property and approximate fixed point property for nonlinear maps in metric spaces without global completeness are established in this paper. …”
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Fixed Point Results for Rational Orbitally (Θ,δb)-Contractions with an Application by Zhenhua Ma, Jamshaid Ahmad, Abdullah Eqal Al-Mazrooei, Durdana Lateef

“…The purpose of this paper is to define a rational orbitally (Θ,δb)-contraction and prove some new results in the context of b-metric spaces. Our results extend, generalize, and unify some known results in the literature. …”
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Fixed Points for ψ-Graphic Contractions with Application to Integral Equations by N. Hussain, S. Al-Mezel, P. Salimi

“…The aim of this paper is to define modified weak α-ψ-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangular α-admissibility. …”
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Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions by Hassen Aydi, Erdal Karapınar, İnci M. Erhan

“…We prove coupled coincidence point and coupled fixed point results of 𝐹∶𝑋×𝑋→𝑋 and 𝑔∶𝑋→𝑋 involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. …”
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The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps by Wei-Shih Du, Erdal Karapınar, Naseer Shahzad

“…We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.…”
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Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self-Mappings with a Partial Order by M. De la Sen

“…This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. …”
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Global Optimal Solutions for Proximal Fuzzy Contractions Involving Control Functions by Abdelhamid Moussaoui, Nawab Hussain, Said Melliani

“…In this study, we introduce new concepts of α−FZ-contraction and α−ψ−FZ-contraction and we discuss existence results of the best proximity points of such types of non-self-mappings involving control functions in the structure of complete fuzzy metric spaces. Our results extend, generalize, enrich, and improve diverse existing results in the current literature.…”
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Admissible Almost Type Z-Contractions and Fixed Point Results by Said Melliani, Abdelhamid Moussaoui, L. S. Chadli

“…In this paper, we introduce a new concept of α-admissible almost type Z-contraction and prove some fixed point results for this new class of contractions in the context of complete metric spaces. The presented results generalize and unify several existing results in the literature.…”
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On Multivalued Hybrid Contractions with Applications by Monairah Alansari, Shehu Shagari Mohammed, Akbar Azam, Nawab Hussain

“…Recently, a notion of b-hybrid contraction for single-valued mappings in the framework of b-metric spaces which unify and improve several significant existing results in the corresponding literature was introduced. …”
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Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions by Iram Iqbal, Nawab Hussain, Hamed H. Al-Sulami, Shanza Hassan

“…The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. …”
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Discussion on Generalized-(αψ, βφ)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems by Maher Berzig, Erdal Karapınar, Antonio-Francisco Roldán-López-de-Hierro

“…This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. …”
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Common Fixed Points of (α,η) − (θ,ϝ) Rational Contractions with Applications by Mujahid Abbas, Hira Iqbal, Manuel De La Sen

“…We present the notion of set valued (α,η)-(θ,ϝ) rational contraction mappings and then some common fixed point results of such mappings in the setting of metric spaces are established. Some examples are presented to support the concepts introduced and the results proved in this paper. …”
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Related Fixed Point Theorems via General Approach of Simulations Functions by Kastriot Zoto, Nabil Mlaiki, Hassen Aydi

“…In this work, we extend and complement some results in view of general and wider structures, such as b−metric spaces. By considering existing classes of Ζ−contractions and Ψ−simulating functions with a solid impact in database results of fixed point theory, we introduce a new general class of simulating functions, called as Ψ−s simulation functions, and also types of κψ−s− contractions in a more general framework. …”
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