We develop an analysis of wavelets and pseudodifferential operators on multidimen-sional ultrametric spaces which are defined as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and Lizorkin generalized functions on multidimensional ultrametric spaces. We also consider some family of pseudodifferential operators on multidimensional ...

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

The aim of this work is to prove the existence and uniqueness Drazin inverse DMP inverses a bounded finite potent endomorphism. In particular, we give main properties these generalized inverses, offer their relationships with adjoint operator, study spectrum, compute respective traces determinants relate operator classical definitions inverse. Moreover, different Moore-Penrose are studied.

This paper deals with the study of some operator inequalities involving the power q-bounded operators along with the most known properties and results, in the more general framework of locally convex vector spaces.

Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L′(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounde...

In this note we investigate generalized projections in Banach algebras. Our results generalize results obtained for bounded linear operators on Hilbert spaces.

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compa...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...