In this paper we study the W -weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W -weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W -weighted Drazin inverse is uniformly o...

We employ the Borsuk-Krasnoselskii antipodal theorem to prove a new fixed point theorem in ordered Banach spaces. Then, the applicability of the result is shown by presenting sufficient conditions for the existence of solutions to initial value problems for first-order difference equations in Banach spaces. To prove that result we shall employ set valued analysis techniques.

This paper will introduce and prove several theorems involving the separation of convex sets by hyperplanes, along with other interesting related results. It will begin with some basic separation results in Rn, such as the Hyperplane Separation Theorem of Hermann Minkowski, and then it will focus on and prove the extension of this theorem into normed vector spaces, known as the Hahn-Banach Sepa...

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

A noncommutative version of the Banach-Stone theorem (II). Abstract In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we give a partial answere to the question 2.1 of [13], and we prove that the structure of the postliminal C *-algebras A determines the topology of its primitive ideals space.

We investigate the computable content of certain theorems which are sometimes called the “principles” of the theory of Banach spaces. Among these the main theorems are the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also study closely related theorems, as Banach’s Inverse Mapping Theorem, the Theorem on Condensation of Singularities and the BanachStein...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

‎In this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex Banach space‎. ‎The results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.