Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets by Luděk Zajíček, Miroslav Zelený

“…This general theorem is also applied to ball small sets in Hilbert spaces and to σ-cone-supported sets in separable Banach spaces.…”
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Local existence result of the single dopant diffusion including cluster reactions of high order by R. Bader, W. Merz

“…The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. …”
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Infinite System of Differential Equations in Some Spaces by M. Mursaleen, Abdullah Alotaibi

“…In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .…”
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On the Scottish Book Problem 155 by Mazur and Sternbach by Mori, Michiya

“…Problem 155 of the Scottish Book asks whether every bijection $U\colon X\rightarrow Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. …”
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Stability of a Quartic Functional Equation by Abasalt Bodaghi

“…We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.…”
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Fixed point theorems for a sum of two mappings in locally convex spaces by P. Vijayaraju

“…Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. …”
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A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems by Yekini Shehu

“…Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.…”
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On the Stability of Quadratic Functional Equations by Jung Rye Lee, Jong Su An, Choonkil Park

“…Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.…”
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On σ-porous sets in abstract spaces by L. Zajíček

“…The main aim of this survey paper is to give basic information about properties and applications of σ-porous sets in Banach spaces (and some other infinite-dimensional spaces). …”
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Greedy algorithms: a review and open problems by Andrea García

“…Next, we provide a general overview of the thresholding greedy algorithm and the Chebyshev thresholding greedy algorithm, with particular attention to their applications to bases in p-Banach spaces with 0 < p ≤ 1 $0< p\leq 1$ . In both cases, we conclude by posing several questions for future research.…”
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Existence and Compactness Results for a System of Fractional Differential Equations by Cheikh Guendouz, Jamal Eddine Lazreg, Juan J. Nieto, Abdelghani Ouahab

“…The existence and uniqueness, boundedness, and continuous dependence of solutions for fractional differential equations with Caputo fractional derivative is proven by Perov’s fixed point theorem in vector Banach spaces. We study the existence and compactness of solution sets and the u.s.c. of operator solutions.…”
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Graph Convergence and Iterative Approximation of Solution of a Set-Valued Variational Inclusions by Faizan Ahmad Khan, Sanjeev Gupta

“…As an application, we consider a set-valued variational inclusion problem (SVIP) in real Banach spaces. Furthermore, we propose an iterative scheme involving the above class of proximal-point mapping to find a solution of SVIP and discuss its convergence under some convenient assumptions. …”
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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

“…The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.…”
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Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology by Marian Nowak

“…Let X be a completely regular Hausdorff space and let E,·E and (F,·F) be Banach spaces. Let Cb(X,E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology βσ. …”
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Norm Attaining Arens Extensions on ℓ1 by Javier Falcó, Domingo García, Manuel Maestre, Pilar Rueda

“…We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ℓ1 with the property that only some fixed Arens extensions determined a priori attain their norms. …”
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Strong laws of large numbers for arrays of row-wise exchangeable random elements by Robert Lee Taylor, Ronald Frank Patterson

“…Let {Xnk,1≤k≤n,n≤1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n−1/p∑k=1nXnk,1≤p<2, is obtained under varying moment and distribution conditions on the random elements. …”
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Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators by C. E. Chidume, N. Djitté

“…An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation Au=0 where A is a bounded m-accretive operator on certain real Banach spaces E that include Lp spaces 2≤p<∞. The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. …”
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Common Fixed Points of Multistep Noor Iterations with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings by S. Imnang, S. Suantai

“…We introduce a general iteration scheme for a finite family of generalized asymptotically quasi-nonexpansive mappings in Banach spaces. The new iterative scheme includes the multistep Noor iterations with errors, modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor, and Khan and Takahashi scheme as special cases. …”
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On the Bishop-Phelps-Bollobás Property for Numerical Radius by Sun Kwang Kim, Han Ju Lee, Miguel Martín

“…We study the Bishop-Phelps-Bollobás property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu. Among other results, we show that L1μ-spaces have this property for every measure μ. …”
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Notes about Quasi-Mixing Operators by Mansooreh Moosapoor, Ismail Nikoufar

“…We prove that quasi-mixing operators exist on all finite-dimensional and infinite-dimensional  Banach spaces. We also prove that an invertible operator $T$ is quasi-mixing if and only if $T^{-1}$ is quasi-mixing. …”
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