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Register a new userIntegral transforms defined by a new fractional class of analytic function in a complex Banach space
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In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.
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In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fractional operators are illustrated.
Given a domain $Omega$ in $mathbb{C}^n$ and a collection of test functions $Psi$ on $Omega$, we consider the complex-valued $Psi$-Schur-Agler class associated to the pair $(Omega,,Psi)$. In this article, we characterize interpolating sequences for the associated Banach algebra of which the $Psi$-Schur-Agler class is the closed unit ball. When $Omega$ is the unit disc $mathbb{D}$ in the complex plane $mathbb{C}$ and the class of test function includes only the identity function on $mathbb{D}$, the aforementioned algebra is the algebra of bounded holomorphic functions on $mathbb{D}$ and in this case, our characterization reduces to the well known result by Carleson. Furthermore, we present several other cases of the pair $(Omega,,Psi)$, where our main result could be applied to characterize interpolating sequences which also show the efficacy of our main result.
We construct a family $(mathcal{X}_al)_{alle omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $mathcal{X}_al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$.
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution equations of order $alphain (1,2]$ associated with the infinitesimal generator of an operator fractional cosine function generated by bounded time-dependent perturbations in a Banach space. We show that the abstract fractional Cauchy problem associated with the infinitesimal generator $A$ of a strongly continuous fractional cosine function remains uniformly well-posed under bounded time-dependent perturbation of $A$. We also provide some necessary special cases.
In this short note, we first consider some inequalities for comparison of some algebraic properties of two continuous algebra-multiplications on an arbitrary Banach space and then, as an application, we consider some very basic observations on the space of all continuous algebra-multiplications on a Banach space.
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