Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings by M. De la Sen

“…Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. …”
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On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems by Ahmed Fadili, Hamid Bounit

“…We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a C0-semigroup. …”
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Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators by Baode Li, Dachun Yang, Wen Yuan

“…The authors also obtain the finite atomic decomposition characterization of HAφ(ℝn), and, as an application, the authors prove that, for a given admissible triplet (φ,q,s), if T is a sublinear operator and maps all (φ,q,s)-atoms with q<∞ (or all continuous (φ,q,s)-atoms with q=∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from HAφ(ℝn) to ℬ. …”
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Subdifferential Properties of Minimal Time Functions Associated with Set-Valued Mappings with Closed Convex Graphs in Hausdorff Topological Vector Spaces by Messaoud Bounkhel

“…Our results extend many existing results, from Banach spaces and normed vector spaces to Hausdorff topological vector spaces (Bounkhel, 2012; Bounkhel and Thibault, 2002; Burke et al., 1992; He and Ng, 2006; and Jiang and He 2009). …”
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Extended Newton-type Method for Nonsmooth Generalized Equation under n,α-point-based Approximation by M. Z. Khaton, M. H. Rashid

“…Let X and Y be Banach spaces and Ω⊆X. Let f:Ω⟶Y be a single valued function which is nonsmooth. …”
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Approximating Common Fixed Points for a Finite Family of Asymptotically Nonexpansive Mappings Using Iteration Process with Errors Terms by Seyit Temir, Adem Kiliçman

“…Let X be a real Banach space and K a nonempty closed convex subset of X. …”
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Partitioning Functional of a Class of Convex Bodies by Xinling Zhang

“…However, estimating the partitioning functionals of general convex bodies in finite dimensional Banach spaces is challenging, so we will begin with the estimation of partitioning functionals for special convex bodies. …”
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Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers by Awad A. Bakery, Afaf R. Abou Elmatty

“…Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.…”
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On Chung-Teicher type strong law for arrays of vector-valued random variables by Anna Kuczmaszewska

“…Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.…”
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Convexities and Existence of the Farthest Point by Z. H. Zhang, C. Y. Liu

“…Five counterexamples are given, which show relations among the new convexities and some important convexities in Banach space. Under the assumption that Banach space 𝑋 is nearly very convex, we give a sufficient condition that bounded, weakly closed subset of 𝑋 has the farthest points. …”
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Convergence Analysis of an Accelerated Iteration for Monotone Generalized α-Nonexpansive Mappings with a Partial Order by Yi-An Chen, Dao-Jun Wen

“…In this paper, we introduce a new accelerated iteration for finding a fixed point of monotone generalized α-nonexpansive mapping in an ordered Banach space. We establish some weak and strong convergence theorems of fixed point for monotone generalized α-nonexpansive mapping in a uniformly convex Banach space with a partial order. …”
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Lipschitz measures and vector-valued Hardy spaces by Magali Folch-Gabayet, Martha Guzmán-Partida, Salvador Pérez-Esteva

“…We define certain spaces of Banach-valued measures called Lipschitz measures. When the Banach space is a dual space X*, these spaces can be identified with the duals of the atomic vector-valued Hardy spaces HXp(ℝn), 0<p<1. …”
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A Note on Generalized Approximation Property by Antara Bhar, Manjul Gupta

“…We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. …”
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A Complete Normed Space of a Class of Guage Integrable Functions by Yassin Alzubaidi

“…The space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. …”
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A *-mixing convergence theorem for convex set valued processes by A. de Korvin, R. Kleyle

“…In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. …”
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A Note on Property (gb) and Perturbations by Qingping Zeng, Huaijie Zhong

“…An operator T∈ℬ(X) defined on a Banach space X satisfies property (gb) if the complement in the approximate point spectrum σa(T) of the upper semi-B-Weyl spectrum σSBF+-(T) coincides with the set Π(T) of all poles of the resolvent of T. …”
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Chaos and shadowing around a homoclinic tube by Yanguang (Charles) Li

“…Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. …”
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Existence and decay of solutions of some nonlinear parabolic variational inequalities by Mitsuhiro Nakao, Takashi Narazaki

“…This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: <u′(t)+Au(t)+Bu(t)−f(t),   v(t)−u(t)>≧0for ∀v∈Lp([0,∞);V)(p≧2) with v(t)∈K a.e. in [0,∞), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. …”
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Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A by Shirin Tavkoli, Rasoul Abazari, Ali Jabbari

“…In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓpX,A. Specifically, we establish that ℓpX,A possesses the BSE property if and only if X is finite and A is BSE. …”
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Well-posedness of the difference schemes of the high order of accuracy for elliptic equations by Allaberen Ashyralyev, Pavel E. Sobolevskiĭ

“…It is well known the differential equation −u″(t)+Au(t)=f(t)(−∞<t<∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E)=C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ‖ϕ‖C(E)=sup⁡−∞<t<∞‖ϕ(t)‖E. …”
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