Perturbations of Regularized Determinants of Operators in a Banach Space by Michael Gil

“…Let be a separable Banach space with the approximation property. For an integer , let be a quasinormed ideal of compact operators in with a quasinorm , such that , where are the eigenvalues of and is a constant independent of . …”
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A Generalization of Uniformly Extremely Convex Banach Spaces by Suyalatu Wulede, Wurichaihu Bai, Wurina Bao

“…We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. …”
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On the mild solutions of higher-order differential equations in Banach spaces by Nguyen Thanh Lan

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On Convergence Theorems for Generalized Alpha Nonexpansive Mappings in Banach Spaces by Buthinah A. Bin Dehaish, Rawan K. Alharbi

“…Furthermore, the same results are established with the Ishikawa iteration process in the uniformly convex Banach space setting. The presented results expand and refine many of the recently reported results in the literature.…”
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On boundary value problems for degenerate differential inclusions in Banach spaces by Valeri Obukhovskii, Pietro Zecca

“…We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. …”
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On the range of the derivative of a smooth mapping between Banach spaces by Robert Deville

“…We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of ℒ(X,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f′(X)=A. …”
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Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces by X. J. Wan, Y. P. Zhang, J. T. Sun

“…We investigate the controllability of impulsive neutral functional differential inclusions in Banach spaces. Our main aim is to find an effective method to solve the controllability problem of impulsive neutral functional differential inclusions with multivalued jump sizes in Banach spaces. …”
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Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces by Satit Saejung, Pongsakorn Yotkaew

“…We discuss the approximation method of finding a common fixed point of two certain mappings defined on a Banach space. This paper deals with three modes of convergence, namely, weak, strong, and △-convergences in the presence of the uniform convexity of the norm. …”
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On non-midpoint locally uniformly rotund normability in Banach spaces by A. K. Mirmostafaee

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Double-dual types over the Banach space C(K) by Markus Pomper

“…Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K, with the sup-norm. …”
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Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces by Junaid Ahmad, Kifayat Ullah, Muhammad Arshad, Manuel de la Sen

“…In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. …”
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A New Characterization of k-Uniformly Rotund Banach Space by Suyalatu Wulede, Tingting Li, Xuan Qin

“…A new characterization of k-uniformly rotund Banach space with 1<P<+∞ is given. Moreover, a corresponding result in the locally k-uniformly rotund Banach space with 1<P<+∞ is given.…”
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Algorithms for a System of General Variational Inequalities in Banach Spaces by Jin-Hua Zhu, Shih-Sen Chang, Min Liu

“…The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. …”
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Spectral integration and spectral theory for non-Archimedean Banach spaces by S. Ludkovsky, B. Diarra

“…There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebra ℒ(E) of the continuous linear operators on a free Banach space E generated by projectors. …”
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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). …”
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Convex Sweeping Processes with Noncompact Perturbations and with Delay in Banach Spaces by A. G. Ibrahim, F. Aladsani

“…We prove two results concerning the existence of solutions for functional differential inclusions that are governed by sweeping processes, with noncompact valued perturbations in Banach spaces. Indeed, we have two goals. The first is to give a technique that allows considering sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time. …”
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Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces by Messaoud Bounkhel

“…In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces. They proved, in p-uniformly convex and q-uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. …”
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New Characterizations of k-Uniformly Extremely Convex Banach Spaces by Suyalatu Wulede

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The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces by Rabian Wangkeeree

“…Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. …”
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The Multivariate Müntz-Szasz Problem in Weighted Banach Space on Rn by Xiangdong Yang

“…The purpose of this paper is to give an extension of Müntz-Szasz theorems to multivariable weighted Banach space. Denote by {λk=(λk1,λk2,...,λkn)}k=1∞ a sequence of real numbers in R+n. …”
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