Band 47, Heft 4

A correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kähler manifold is shown.

The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.

This paper investigates the preservation of hopficity and co-hopficity on passing to finite-index subsemigroups and extensions. It was already known that hopficity is not preserved on passing to finite Rees index subsemigroups, even in the finitely generated case. We give a stronger example to show that it is not preserved even in the finitely presented case. It was also known that hopficity is not preserved in general on passing to finite Rees index extensions, but that it is preserved in the finitely generated case. We show that, in contrast, hopficity is not preserved on passing to finite Green index extensions, even within the class of finitely presented semigroups. Turning to co-hopficity, we prove that within the class of finitely generated semigroups, co-hopficity is preserved on passing to finite Rees index extensions, but is not preserved on passing to finite Rees index subsemigroups, even in the finitely presented case. Finally, by linking co-hopficity for graphs to co-hopficity for semigroups, we show that without the hypothesis of finite generation, co-hopficity is not preserved on passing to finite Rees index extensions.

For any non-negative integers m and n, we define the classes of m-ω 1 -p ω+n - projective groups and strongly m-ω 1 -p ω+n -projective groups, which properly encompass the classes of ω 1 -p ω+n -projectives introduced by Keef in J. Algebra Numb. Th. Acad. (2010) and strongly ω 1 -p ω+n -projectives introduced by the present author in Hacettepe J. Math. Stat. (2014), respectively. The new group structures share many interesting properties, which are closely related to these of the aforementioned two own subclasses. Moreover, certain basic results in this direction are also established.

In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.

In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.

In this paper, we shall study estimates for the coefficients an, n = 1,2 of a class of univalent harmonic mappings defined on the exterior of the unit disk Ũ = { z : |z| > 1 }, which keep infinity fixed. For this purpose, we apply Faber polynomials and an inequality of the Grunsky type.

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

We consider the Z. Szmydt problem for the hyperbolic functional differential equation. We prove a theorem on existence of a unique classical solution and the Carathéodory solution of the hyperbolic equation.

The pointwise estimates of the deviations r T͂n,A,Bf (·) - f͂͂ (·) and T͂n,A,Bf (·) - f͂͂ (·,ε) in terms of moduli of continuity ω̃f and r ω̃f are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal [3, Theorem 1, p. 437].

Sufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.

In this paper, we present a generalization of the notion of bounded slope variation for functions defined on a rectangle I b a in ℝ 2 . Given a strictly increasing function µ-defined in a closed real interval, we introduce the class BV µ,2 (I b a ), of functions of bounded second µ-variation on I b a ; and show that this class can be equipped with a norm with respect to which it is a Banach space. We also deal with the important case of factorizable functions in BV µ,2 (I b a ) and finally we exhibit a relation between this class and the one of double Riemann-Stieltjes integrals of functions of bi-dimensional bounded variation.

In this paper, we consider the Nemytskii operator (Hf)(t) = h(t, f(t)), generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α)-variation (with respect to a weight function α) into the space of functions of bounded (q,2,α)-variation (with respect to α) 1<q<p, then H is of the form (Hf)(t) = A(t)f(t)+B(t). On the other hand, if 1<p<q then H is constant. It generalize several earlier results of this type due to Matkowski-Merentes and Merentes. Also, we will prove that if a uniformly continuous Nemytskii operator maps a space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611-620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.

In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results.

In this paper, a general coincidence and common fixed points theorem for two hybrid pairs of mappings satisfying property (E.A) is proved, generalizing the main results from [3] and [9].

A. Lewandowski and H. Makowiecka proved in 1979 that existence of the Havlicek-Tietze configuration (shortly H-T) in the desarguesian projective plane is equivalent to existence in the associated field, a root of polynomial x 2 + x + 1, different from 1. We show that such a configuration exists in every projective plane over Galois field GF(p 2 ) for p≠3. As it has been demonstrated, in a projective plane over arbitrary field F, each hexagon contained in H-T, satisfies the Pappus-Pascal axiom, even if F is noncommutative. Moreover, such a hexagon either is pascalian or has exactly one pair of opposite sides intersecting at a point collinear with two points not belonging to these sides. In particular, all such hexagons are pascalian iff charF=2. For the (noncommutative) field of quaternions, we have determined the set of all roots of the mentioned polynomial. Every H -T is the special Pappus configuration, in which three main diagonals of the hexagon are concurrent.

It is proved that the Banach-Mazur distance between arbitrary two convex quadrangles is at most 2. The distance equals 2 if and only if the pair of these quadrangles is a parallelogram and a triangle.

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.

In this paper, the topologies underlying a product Frölicher space and a coproduct Frölicher space are defined and compared. It is shown that the product topology, which is equal to the one induced by structure functions, is the weakest one in which all projections are continuous. On the other hand, it is proved that the three topologies arising from the coproduct structure are equal.