Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications by Mujahid Abbas, Hira Iqbal, Adrian Petrusel

“…In this paper, we will introduce the concept of Suzuki type multivalued (θ,R)-contraction and we will prove some fixed point results in the setting of a metric space equipped with a binary relation. Our results generalize and extend various comparable results in the existing literature. …”
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Note on limits of simply continuous and cliquish functions by Janina Ewert

“…The main result of this paper is that any function f defined on a perfect Baire space (X,T) with values in a separable metric space Y is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence {fn:n≥1} of simply continuous functions. …”
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Li-Yorke Sensitivity of Set-Valued Discrete Systems by Heng Liu, Fengchun Lei, Lidong Wang

“…Consider the surjective, continuous map f:X→X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 𝒦(X) is the space of all nonempty compact subsets of X endowed with the Hausdorff metric. …”
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Lipschitz Operators Associated with Weakly $p$-Compact and Unconditionally $p$-Compact Sets by Ramazan İnal, Ayşegül Keten Çopur

“…The primary method used to obtain the results in the study is the linearization of Lipschitz operators through the Lipschitz-free space constructed over a pointed metric space.…”
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Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions by Shazia Kanwal, Akbar Azam

“…The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. …”
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Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle by Yaoyao Lan, Chunlai Mu

“…Let X denote a compact metric space and let f : X→X be a continuous map. It is known that a discrete dynamical system (X,f) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X. …”
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A porosity result in convex minimization by P. G. Howlett, A. J. Zaslavski

“…We study the minimization problem f(x)→min, x∈C, where f belongs to a complete metric space ℳ of convex functions and the set C is a countable intersection of a decreasing sequence of closed convex sets Ci in a reflexive Banach space. …”
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Restrictive metric regularity and generalized differential calculus in Banach spaces by Boris S. Mordukhovich, Bingwu Wang

“…We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯) is not surjective. …”
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A Geometric Fuzzy-Based Approach for Airport Clustering by Maria Nadia Postorino, Mario Versaci

“…By representing each airport as a point in the given reference metric space, the geometric distance among airports—which corresponds to a measure of similarity—has in fact an intrinsic fuzzy nature due to the airport specific characteristics. …”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form  0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. …”
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MDTR: a knowledge-guided interpretable representation for quantifying liver toxicity at transcriptomic level by Inyoung Sung, Sangseon Lee, Dongmin Bang, Dongmin Bang, Jungseob Yi, Sunho Lee, Sun Kim, Sun Kim, Sun Kim, Sun Kim

“…In addition, MDTR shows interpretability at the level of DILI mechanisms in terms of the distance, i.e., in a metric space. Furthermore, we provided a user-friendly and freely accessible website (http://biohealth.snu.ac.kr/software/MDTR), enabling users to easily measure DILI in drug-induced transcriptome data.…”
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