Acta et Commentationes Universitatis Tartuensis de Mathematica

On a class of vector-valued entire Dirichlet series in n variables

2018-11-21T06:12:44+00:00

We consider a class F of entire Dirichlet series in n variables, whose coefficients belong to a commutative Banach algebra E. With a well defined norm, F is proved to be a Banach algebra with identity. Further results on quasi-invertibility, spectrum and continuous linear functionals are proved for elements belonging to F.

Quasi-monomiality and operational identities for Laguerre–Konhauser-type matrix polynomials and their applications

2018-11-21T06:12:45+00:00

It is shown that an appropriate combination of methods, relevant to matrix polynomials and to operational calculus can be a very useful tool to establish and treat a new class of matrix Laguerre–Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Laguerre–Konhauser matrix polynomials and discuss the links with classical polynomials.

Complete asymptotics of the approximation of function from the Sobolev classes by the Poisson integrals

2018-11-21T06:12:44+00:00

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Stability in higher-order nonlinear fractional differential equations

2018-11-21T06:12:43+00:00

We give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of higher-order nonlinear fractional differential equations. By using Krasnoselskii's xed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that f (t, 0) = 0. The results obtained here generalize the work of Ge and Kou.

Applications of Chebyshev polynomials on a Sakaguchi type class of analytic functions associated with quasi-subordination

2018-11-21T06:12:42+00:00

We introduce a class of analytic functions which is defined in terms of a quasi-subordination. Coefficient estimates including the relevant classical Fekete–Szegö inequality of functions belonging to the aforementioned class are derived. Improved results for associated classes involving subordination and majorization are also discussed.

Remarks on locally closed set

2018-11-21T06:12:42+00:00

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On Lucas-balancing zeta function

2018-11-21T06:12:41+00:00

In the present study a new modication of Riemann zeta function known as Lucas-balancing zeta function is introduced. The Lucas-balancing zeta function admits its analytic continuation over the whole complex plane except its poles. This series converges to a fixed rational number − ½ at negative odd integers. Further, in accordance to Dirichlet L-function, the analytic continuation of Lucas-balancing L-function is also discussed.

Equivalence results for implicit Jungck–Kirk type iterations

2018-11-21T06:12:41+00:00

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included.

Biot number effect on MHD flow and heat transfer of nanofluid with suspended dust particles in the presence of nonlinear thermal radiation and non-uniform heat source/sink

2018-11-21T06:12:40+00:00

This paper considers the problem of steady, boundary layer flow and heat transfer of dusty nanofluid over a stretching surface in the presence of non-uniform heat source/sink and nonlinear thermal radiation with Biot number effect. The base fluid (water) is considered with silver (Ag) nanoparticles along with suspended dust particles. The governing equations in partial form are reduced to a system of non-linear ordinary differential equations using suitable similarity transformations. An effective Runge–Kutta–Fehlberg fourth-fifth order method along with shooting technique is used for the solution. The effects of flow parameters such as nanofluid interaction parameter, magnetic parameter, solid volume fraction parameter, Prandtl number, heat source/sink parameters, radiation parameter, temperature ratio parameter and Biot number on the flow field and heat-transfer characteristics were obtained and are tabulated. Useful discussions were carried out with the help of plotted graphs and tables. Under the limiting cases, comparison with the existing results was made and found to be in good agreement.

On commutativity of semiprime Banach algebras

2018-11-21T06:12:39+00:00

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An entire function sharing fixed points with its linear differential polynomial

2018-11-21T06:12:39+00:00

We study the uniqueness of entire functions, when they share a linear polynomial, in particular, fixed points, with their linear differential polynomials.

A new approach to nearly compact spaces

2018-11-21T06:12:38+00:00

Using the covers formed by pre-open sets, we introduce and study the notion of po-compactness in topological spaces. The notion of po-compactness is weaker than that of compactness but stronger than semi-compactness. It is observed that po-compact spaces are the same as nearly compact spaces. However, we find new characterizations to near compactness, when we study it in the sense of po-compactness.

Summands in locally almost square and locally octahedral spaces

2018-11-21T06:12:37+00:00

We study the question whether properties like local/weak almost squareness and local octahedrality pass down from an absolute sum X ⊕_F Y to the summands X and Y.