$K$-$b$-Frames for Hilbert Spaces and the $b$-Adjoint Operator by Chaimae Mezzat, Samir Kabbaj

“…The idea is to take a sequence from a Banach space and see how it can be a frame for a Hilbert space. …”
Get full text

Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers by Ahmet Faruk Çakmak, Feyzi Başar

“…Later, we define the space C*(Ω) of *-continuous functions and state that it forms a vector space with respect to the non-Newtonian addition and scalar multiplication and we prove that C*(Ω) is a Banach space. Finally, Multiplicative calculus (MC), which is one of the most popular non-Newtonian calculus and created by the famous exp function, is applied to complex numbers and functions to investigate some advance inner product properties and give inclusion relationship between C*(Ω) and the set of C*′(Ω)*-differentiable functions.…”
Get full text

The Fixed Point Property in c0 with an Equivalent Norm by Berta Gamboa de Buen, Fernando Núñez-Medina

“…We study the fixed point property (FPP) in the Banach space c0 with the equivalent norm ‖⋅‖D. The space c0 with this norm has the weak fixed point property. …”
Get full text

Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. …”
Get full text

Flow invariance for perturbed nonlinear evolution equations by Dieter Bothe

“…Let X be a real Banach space, J=[0,a]⊂R, A:D(A)⊂X→2X\ϕ an m-accretive operator and f:J×X→X continuous. …”
Get full text

On the convergence of Fourier series by Geraldo Soares de Souza

“…Bp is endowed with the norm ‖f‖Bp=Int∑n=0∞|cn|, where the infimum is taken over all possible representations of f. Bp is a Banach space for 1/2<p<∞. Bp is continuously contained in Lp for 1≤p<∞, but different. …”
Get full text

Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation by Kenneth L. Jones, Xiaogui He, Yunkai Chen

“…The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. …”
Get full text

Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions by Bashir Ahmad, Juan J. Nieto

“…The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.…”
Get full text

Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations by Valentin Keyantuo, Carlos Lizama, Mahamadi Warma

“…When A is the generator of a C0-semigroup (T(t))t≥0 on a Banach space X, we obtain an explicit representation of mild solutions of the above problem in terms of the semigroup. …”
Get full text

Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…This paper is concerned with positive α-times resolvent families on an ordered Banach space E (with normal and generating cone), where 0<α≤2. …”
Get full text

Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses by Zhenguo Luo, Liping Luo, Jianhua Huang, Binxiang Dai

“…By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. …”
Get full text

A representation theorem for operators on a space of interval functions by J. A. Chatfield

“…Suppose N is a Banach space of norm |•| and R is the set of real numbers. …”
Get full text

A weak invariance principle and asymptotic stability for evolution equations with bounded generators by E. N. Chukwu, P. Smoczynski

“…If V is a Lyapunov function of an equation du/dt=u′=Zu in a Banach space then asymptotic stability of an equilibrium point may be easily proved if it is known that sup(V′)<0 on sufficiently small spheres centered at the equilibrium point. …”
Get full text

Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem by Ya-Ning Li, Hong-Rui Sun

“…We show that A generates an exponentially bounded (α,β)-ROF on a Banach space X if and only if the problem has a unique exponentially bounded classical solution vx and Avx∈L loc 1(ℝ+,X). …”
Get full text

A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings by Suwicha Imnang, Suthep Suantai

“…Let X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. …”
Get full text

A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities by Teffera M. Asfaw

“…Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X⁎. …”
Get full text