Abstract. By making use of the generalized hypergeometric functions, in this paper we introduce and investigate certain new subclasses of analytic functions of complex order defined in the open unit disk. Coefficient inequalities, radii of close-to-convexity, starlikeness and convexity, closure theorems, integral means inequalities and several relations associated with (n, δ)-neighborhood for t...

In this paper, we introduce operator s-convex functions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

Let F be a monotone operator on the complete lattice L into itself. Tarski's lattice theoretical fixed point theorem states that the set of fixed points of F is a nonempty complete lattice for the ordering of L. We give a constructive proof of this theorem showing that the set of fixed points of F is the image of L by a lower and an upper preclosure operator. These preclosure operators are the ...

Abstract We present an example of a densely defined, linear operator on the $$l^{1}$$ l 1 space with property that each basis vector standard Schauder does not belong to its domain. Our is based construction Markov chain all states instantaneous given by D. Blackwell in...

In Part I of [3], Adaricheva and Nation introduced a new property that holds (dually) for the natural equaclosure operator on congruence lattices of semilattices with operators, and hence holds in lattices of quasivarieties Lq(K). The new property implied some previously known conditions as well. Using the duality for congruences of semilattices with operators from [7], we will refine that to a...

LetW (A) andWe(A) be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A1, . . . , Am) acting on an infinite dimensional Hilbert space, respectively. In this paper, it is shown that We(A) is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ {1, . . . ,m}, We(A) can be obtained as the intersection ...

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex representation of the operator which is a fixed point of this conjugation. 2000 Mathematics Subject Classification: 47H05 keywords: maximal monotone operators, conjugat...

For a set S in a Banach space, we denote by dim(S) its covering dimension [1, p. 42]. Recall that, when S is a convex set, the covering dimension of S coincides with the algebraic dimension of S, this latter being understood as ∞ if it is not finite [1, p. 57]. Also, S and conv(S) will denote the closure and the convex hull of S, respectively. In [3], we proved what follows. dim({x ∈ X : Φ(x) =...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...