In this paper we deal with methods for finding zeroes of set-valued operators A in Banach spaces. The first aim of this note is to show that the Yosida regularization may be combined with the schemes in [1, 2] keeping the strong convergence properties of the iterates and extending to set-valued operators two recent results by Chidume [1] and Chidume and Zegeye [2]. The second goal of the note i...

The set of all nonnegative selfadjoint extensions of a nonnegative linear relation (multi-valued operator) is described by using a partial order defined on the set of the corresponding quadratic forms. This characterization leads to a generalization of a result due to M.G. Krĕın. 2000 Mathematics Subject Classification: 47A06, 47A20, 47B25, 47A63.

Matrix-valued analogues of the little q-Jacobi polynomials are introduced and studied. For the 2 × 2-matrix-valued little q-Jacobi polynomials explicit expressions for the orthogonality relations, Rodrigues formula, three-term recurrence relation and its relation to matrix-valued q-hypergeometric series and the scalar-valued little q-Jacobi polynomials are presented. The study is based on the m...

A dx. Given a Banach space (X, ‖ · ‖) and 1 ≤ p < ∞ we shall denote by L(R, X) the space of Bochner p-integrable functions endowed with the norm ‖f‖Lp(Rn,X) = ( ∫ Rn ‖f(x)‖ dx), by Lc (R , X) the closure of the compactly supported functions in L(R, X) and by Lweak,α(R , X) the space of measurable functions such that |{x ∈ R : ‖f(x)‖ > λ}| ≤ α(λ) where α : R → R is a non increasing function. We ...

Passivity and dissipativity, in Jan Willems’s sense, are known to be powerful tools for stability analysis feedback control design. For instance, passive systems negative interconnection with slope-restricted, static, single-valued, smooth nonlinearities, as Lur’e systems, have been thoroughly studied automatic control, yielding the so-called absolute problem (with famous Popov circle criteria)...

141 Abstract Neutrosophic sets, being generalization of classic sets, fuzzy sets and intuitionistic fuzzy sets, can simultaneously represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. Neutrosophic theory has been developed in twenty first century and not much of arithmetic has been developed for this set. To solve any problem using neutrosophic da...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

Let T be an operator acting on a Banach space X, let σ(T ) and σBW (T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σBW (T ) = σ(T ) \E(T ), where E(T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation poi...