Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications by Veli Shakhmurov

“…The embedding theorems in weighted Besov-Lions type spaces 𝐵𝑙,𝑠𝑝,𝑞,𝛾 (Ω;𝐸0,𝐸) in which 𝐸0,𝐸 are two Banach spaces and 𝐸0⊂𝐸 are studied. The most regular class of interpolation space 𝐸𝛼 between 𝐸0 and E is found such that the mixed differential operator 𝐷𝛼 is bounded from 𝐵𝑙,𝑠𝑝,𝑞,𝛾 (Ω;𝐸0,𝐸) to 𝐵𝑠𝑝,𝑞,𝛾 (Ω;𝐸𝛼) and Ehrling-Nirenberg-Gagliardo type sharp estimates are established. …”
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Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations by Xue Pan, Xiuwen Li, Jing Zhao

“…We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. …”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…Particularly, an existence result without using measure of noncompactness condition is presented in ordered and weakly sequentially complete Banach spaces. These results are very convenient for application. …”
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Random Fixed Point Theorems and Applications to Random First-Order Vector-Valued Differential Equations by Adil El-Ghabi, Abdelmjid Khchine, Mohamed Aziz Taoudi

“…We also discuss the case of monotone random operators in ordered Banach spaces. Our results extend several earlier works, including Itoh’s random fixed point theorem. …”
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Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions by Haiyong Qin, Zhenyun Gu, Youliang Fu, Tongxing Li

“…This paper is concerned with the existence results of nonlocal problems for a class of fractional impulsive integrodifferential equations in Banach spaces. We define a piecewise continuous control function to obtain the results on controllability of the corresponding fractional impulsive integrodifferential control systems. …”
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Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces by Preeyalak Chuadchawna, Ali Farajzadeh, Anchalee Kaewcharoen

“…In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. …”
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Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies 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 defined on X, equipped with the strict topologies βz, where   z=σ,∞,p,τ,t. …”
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Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions by Zhenhai Liu, Maojun Bin

“…We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the PC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. …”
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The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces by Shaoyong Zhang, Meiling Zhang, Yujia Zhan

“…It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. …”
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Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments by Cristóbal González, Antonio Jiménez-Melado

“…In this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0, in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at ∞ as ω(t). …”
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Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application by Mohamed Amine Farid, El Miloudi Marhrani, Mohamed Aamri

“…In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2×2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. …”
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Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach by Sutrima Sutrima, Christiana Rini Indrati, Lina Aryati

“…As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. …”
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Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations by Kifayat Ullah, Sabri T. M. Thabet, Anwar Kamal, Junaid Ahmad, Fayyaz Ahmad

“…We consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. …”
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A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators by Kriengsak Wattanawitoon, Poom Kumam

“…The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-ϕ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. …”
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On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications by S. Amat, C. Bermúdez, S. Busquier, M. J. Legaz, S. Plaza

“…This paper is devoted to the study of a class of high-order iterative methods for nonlinear equations on Banach spaces. An analysis of the convergence under Kantorovich-type conditions is proposed. …”
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Convolution Algebraic Structures Defined by Hardy-Type Operators by Pedro J. Miana, Juan J. Royo, Luis Sánchez-Lajusticia

“…The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products on ℝ+). …”
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On a family of Wiener type spaces by R. H. Fischer, A. T. Gürkanli, T. S. Liu

“…A kind of generalization of the Wiener's definition was given by H.Feichtinger in [2] as a Banach spaces of functions (or measures, distributions) on locally compact groups that are defined by means of the global behaviour of certain local properties of their elements. …”
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Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications by Uamporn Witthayarat, Yeol Je Cho, Poom Kumam

“…The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2)−1(0) and (B+M1)−1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. …”
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The Partial Inner Product Space Method: A Quick Overview by Jean-Pierre Antoine, Camillo Trapani

“…It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases of partial inner product spaces (PIP-spaces). …”
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Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces by Awad A. Bakery, Mustafa M. Mohammed

“…In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. …”
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