On a higher-order evolution equation with a Stepanov-bounded solution by Aribindi Satyanarayan Rao

“…We study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. …”
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Convergence theorems for I-nonexpansive mapping by B. E. Rhoades, Seyit Temir

“…We establish the weak convergence of a sequence of Mann iterates of an I-nonexpansive map in a Banach space which satisfies Opial's condition.…”
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A generalized σ-porous set with a small complement by Jaroslav Tišer

“…We show that in every Banach space, there is a g-porous set, the complement of which is of ℋ1-measure zero on every C1 curve.…”
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Isometries between Spaces of Vector-Valued Differentiable Functions by Alireza Ranjbar-Motlagh

“…This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space.…”
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Approximating fixed points of nonexpansive type mappings by Hemant K. Pathak, Mohammad S. Khan

“…In a uniformly convex Banach space, the convergence of Ishikawa iterates to a unique fixed point is proved for nonexpansive type mappings under certain conditions.…”
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Weak convergence theorem for Passty type asymptotically nonexpansive mappings by B. K. Sharma, B. S. Thakur, Y. J. Cho

“…In this paper, we prove a convergence theorem for Passty type asymptotically nonexpansive mappings in a uniformly convex Banach space with Fréchet-differentiable norm.…”
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On the Existence of Polynomials with Chaotic Behaviour by Nilson C. Bernardes, Alfredo Peris

“…We also study distributional chaos for polynomials and show that every infinite-dimensional separable Banach space supports polynomials of arbitrary positive degree that have a dense distributionally scrambled linear manifold.…”
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Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings by Tanakit Thianwan

“…We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach space E which has a Fréchet differentiable norm or its dual E* has the Kadec-Klee property. …”
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A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings by C. E. Chidume, E. U. Ofoedu

“…Let E be a real Banach space, and K a closed convex nonempty subset of E. …”
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A note on properties that imply the fixed point property by S. Dhompongsa, A. Kaewkhao

“…We give relationships between some Banach-space geometric properties that guarantee the weak fixed point property. …”
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On the Carleman classes of vectors of a scalar type spectral operator by Marat V. Markin

“…The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator's resolution of the identity. …”
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Evolution semigroups for nonautonomous Cauchy problems by Gregor Nickel

“…In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP)  {u˙(t)=A(t)u(t)u(s)=x∈X on a Banach space X by the existence of certain evolution semigroups.…”
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Essential Norm of Operators into Weighted-Type Spaces on the Unit Ball by Pablo Galindo, Mikael Lindström, Stevo Stević

“…The essential norm of any operator from a general Banach space of holomorphic functions on the unit ball in ℂn into the little weighted-type space is calculated. …”
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A note on properties that imply the fixed point property

“…<p>We give relationships between some Banach-space geometric properties that guarantee the weak fixed point property. …”
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On absolutely invertibles by Francisco Javier García-Pacheco, María de los Ángeles Moreno-Frías, Marina Murillo-Arcila

“…Finally, two applications to classical operator theory were provided, i.e., every Banach space of dimension of at least $ 2 $ could be equivalently re-normed in such a way that the group of surjective linear isometries was not a normal subgroup of the group of isomorphisms, and every infinite-dimensional Banach space, containing a proper complemented subspace isomorphic to it, could be equivalently re-normed so that the set of surjective linear operators was not dense in the Banach algebra of bounded linear operators.…”
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Asymptotically Stable Solutions of a Generalized Fractional Quadratic Functional-Integral Equation of Erdélyi-Kober Type by Mohamed Abdalla Darwish, Beata Rzepka

“…We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+). We show that this equation has at least one asymptotically stable solution.…”
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Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions by Shayma Adil Murad, Hussein Jebrail Zekri, Samir Hadid

“…We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.…”
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A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically 𝜙-Strongly Pseudocontractive Mappings by Luigi Muglia, Yonghong Yao

“…In this paper we prove the equivalence and the strong convergence of an explicit Mann iterative process and a modified implicit iterative process for asymptotically 𝜙-strongly pseudocontractive mappings in a uniformly smooth Banach space.…”
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On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation by M. Eshaghi Gordji, H. Baghani, O. Baghani

“…The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space 𝑋∶=𝐶([𝑎,𝑏],ℝ𝑛). Later on, we give some examples of applications of this type of results.…”
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Normed Domains of Holomorphy by Steven G. Krantz

“…We treat the classical concept of domain of holomorphy in ℂn when the holomorphic functions considered are restricted to lie in some Banach space. Positive and negative results are presented. …”
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