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Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
In this paper, we define and study the space of all the functions of bounded variation $f:[x,y]\to \mathbb{Y}$ denoted by $\mathcal{BV}[x,y],$ where $[x,y]$ is an ordered interval and $\mathbb{Y}$ is an absolute order unit space having…
In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy…
The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are…
In this note, we introduce a novel norm, termed the $t-$Berezin norm, on the algebra of all bounded linear operators defined on a reproducing kernel Hilbert space $\mathcal{H}$ as $$\|A\|_{t-ber} = \sup_{ \lambda, \mu \in \Omega} \left\{…
Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…
For a completely distributive quantale $L$, $L$-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous…
We completely characterize smoothness of bounded linear operators between infinite dimensional real normed linear spaces, probably for the very first time, by applying the concepts of Birkhoff-James orthogonality and semi-inner-products in…
We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued $(\in,\ivq)$-fuzzy filters of pseudo $BL$-algebras and…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
After introducing a natural notion of continuous fields of locally convex spaces, we establish a new theory of strongly continuous families of possibly unbounded self-adjoint operators over varying Hilbert spaces. This setting allows to…
The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…
In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…
We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side. It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is…
We consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO(X) into BLO(X), generalizing the…
In this paper an idea of soft linear spaces and soft norm on soft linear spaces are given and some of their properties are studied. Soft vectors in soft linear spaces are introduced and their properties are studied. Completeness of soft…