On nth-order differential operators with Bohr-Neugebauer type property by Aribindi Satyanarayan Rao

“…Suppose B is a bounded linear operator in a Banach space. If the differential operator dndtn−B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov-bounded solution of the differential equation dndtnu(t)−Bu(t)=g(t), u(n−1),…,u′,u are all almost periodic.…”
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The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems by Kriengsak Wattanawitoon, Poom Kumam

“…The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature.…”
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Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space by Qiuju Xing, Yuming Shi

“…This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of maps that have transversal homoclinic orbits and are chaotic in the sense of both Li-Yorke and Devaney with positive topological entropy.…”
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Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument by Shanliang Zhu, Shufang Zhang, Xinli Zhang, Qingling Li

“…Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.…”
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On Linear Difference Equations for Which the Global Periodicity Implies the Existence of an Equilibrium by István Győri, László Horváth

“…It is proved that any first-order globally periodic linear inhomogeneous autonomous difference equation defined by a linear operator with closed range in a Banach space has an equilibrium. This result is extended for higher order linear inhomogeneous system in a real or complex Euclidean space. …”
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Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations by Jia Mu

“…We mainly study the fractional evolution equation in an ordered Banach space 𝑋𝐶𝐷𝑎0+𝑢(𝑡)+𝐴𝑢(𝑡)=𝑓(𝑡,𝑢(𝑡),𝐺𝑢(𝑡)) , 1<𝛼<2, 𝑢(0)=𝑥∈𝑋, 𝑢(0)=𝜃. …”
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On hypersurfaces in a locally affine Riemannian Banach manifold II by El-Said R. Lashin, Tarek F. Mersal

“…In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.…”
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Solvability of integral equations via the technique of measures of noncompactness by Babak Mohammadi, Mohammad Mursaleen, Vahid Parvaneh

“….], we extend here Darbo’s fixed point theorem in a Banach space using the combined technique of Wardowski-Mizoguchi-Takahashi contraction. …”
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Generalized Stability of Euler-Lagrange Quadratic Functional Equation by Hark-Mahn Kim, Min-Young Kim

“…The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equation f(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in (β,p)-Banach space, where a,b are fixed rational numbers such that a≠-1,0 and b≠0.…”
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On ΛpBV-Solutions of Some Nonlinear Integral Equations on the Plane by Jurancy Ereú, Liliana Pérez, Luz Rodríguez

“…In this paper, we define the space of functions Λp-bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, ΛpBVIab,ℝ.…”
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Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components by Luisa Toscano, Speranza Toscano

“…We study the solvability of Dirichlet and Neumann problems for different classes of nonlinear elliptic systems depending on parameters and with nonmonotone operators, using existence theorems related to a general system of variational equations in a reflexive Banach space. We also point out some regularity properties and the sign of the found solutions components. …”
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Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions by Marian Nowak

“…Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. …”
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Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.…”
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Norm Estimates for Solutions of Polynomial Operator Equations by Michael Gil’

“…We consider the equations ∑k=0mcm-kAkXBk=C and ∑k=0mcm-kAkXBm-k=C, where ck∈C  (k=1,…,m), c0=1, A,B,C are given linear bounded operators in a Banach space and X is to be found. Representations of solutions are derived. …”
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Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems by Kamonrat Nammanee, Suthep Suantai, Prasit Cholamjiak

“…We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. …”
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On the surjectivity of linear transformations by M. Damlakhi, V. Anandam

“…Let B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. …”
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Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping by Xian Wang, Jun-min Chen, Hui Tong

“…We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. …”
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Exponential stability for abstract linear autonomous functional differential equations with infinite delay by Jin Liang, Falun Huang, Tijun Xiao

“…Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation x˙(t)=L(xt)                              (∗) where L is a continuous linear operator on some abstract phase space B into a Banach space E. We prove that the solution semigroup of (∗) is exponentially stable if and only if the fundamental operator (∗) is exponentially stable and the phase space B is an exponentially fading memory space.…”
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Discrete Weighted Pseudo-Almost Automorphy and Applications by Zhinan Xia

“…We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. …”
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Strong Laws of Large Numbers for 𝔹-Valued Random Fields by Zbigniew A. Lagodowski

“…Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.…”
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