Some strong differential subordinations using a differential operator

Author: Loriana Andrei / Mitrofan Choban

Abstract: In the present paper we study the operator $RD_{\lambda ,\alpha
}^{n}f(z,\zeta )$ defined by using the extended \linebreak Ruscheweyh derivative $%
R^{n}f(z,\zeta )$ and the extended generalized S\u{a}l\u{a}gean operator $%
D_{\lambda }^{n}f(z,\zeta )$, as $RD_{\lambda ,\alpha }^{n}:\mathcal{A}%
_{\zeta }^{\ast }\rightarrow \mathcal{A}_{\zeta }^{\ast }$, $RD_{\lambda
,\alpha }^{n}f(z,\zeta )=(1-\alpha )R^{n}f(z,\zeta )+\alpha D_{\lambda
}^{n}f(z,\zeta ),$ where $\mathcal{A}_{n\zeta }^{\ast }=\{f\in \mathcal{H}%
(U\times \overline{U}),\ f(z,\zeta )=z+a_{n+1}\left( \zeta \right)
z^{n+1}+\dots ,\ z\in U,$ $\zeta \in \overline{U}\}$\ is the class of
normalized analytic functions with $\mathcal{A}_{1\zeta }^{\ast }=\mathcal{A}%
_{\zeta }^{\ast }.$ We obtain several strong differential
subordinations regarding the extended operator $RD_{\lambda
,\alpha }^{n}$. Some examples are presented. PDF |

No. of downloads: 370

UU rings

Author: Grigore Călugăreanu

Abstract: A new class of rings is studied: rings all whose units are sums $1+n$, for a
suitable nilpotent element $n$. These are called UU rings. PDF |

No. of downloads: 270

On the geometry behind a recurrent relation

Author: Cristian Cobeli / Alexandru Zaharescu

Abstract: We consider a certain linear recursive relation with integer parameters and
study some of its algebraic and geometric properties, with the purpose
of estimating the number of chains of valences in the Farey series. PDF |

No. of downloads: 315

Bounds of the second degree cumulative frontier gaps of functions with generalized convexity

Author: Gabriela Cristescu / Muhammad Aslam Noor / Muhammad Uzair Awan

Abstract: We prove that the set of second degree cumulative frontier gaps, via fractional integrals of positive orders, of twice differentiable functions having generalized convexity at the level of the second derivative is upper bounded. A sharp Hermite-Hadamard type inequality via fractional integrals leads to an evaluation of this upper bound, which does not depend on the order of the fractional integration. Six particular generalized convexity properties are investigated from the point of view of this boundary property. PDF |

No. of downloads: 205

Extensions of Perov theorem

Author: Marija CvetkoviÄ‡ / Vladimir RakoÄeviÄ‡

Abstract: [Perov, A. I., On Cauchy problem for a system of ordinary
diferential equations, (in Russian), Priblizhen. Metody Reshen.
Difer. Uravn., 2 (1964), 115-134] used the concept of
vector valued metric space and obtained a Banach type fixed point
theorem on such a complete generalized metric space. In this
article we study fixed point results for the new extensions of
Banach's contraction principle to cone metric space, and we give
some generalized versions of the fixed point theorem of Perov.
As corollaries some results of [Zima, M., A certain fixed point theorem and its
applications to integral-functional equations, Bull. Austral. Math. Soc., 46 (1992),
179--186] and [Borkowski, M., Bugajewski, D. and Zima, M., On some fixed-point
theorems for generalized contractions and their perturbations, J. Math. Anal. Appl., 367 (2010), 464--475] are generalized for a Banach cone space with a non-normal cone.
The theory is illustrated with some examples. PDF |

No. of downloads: 217

Fixed point theorems for multivalued contractions in Kasahara spaces

Author: Alexandru-Darius Filip

Abstract: In this paper we present some fixed point results for multivalued $\alpha$-contractions. Our results are obtained in a more general setting, the so called Kasahara space. Some of them are generalizations of Maia's type fixed point result for multivalued $\alpha$-contractions. As application, a fixed point theorem for integral inclusions is given. PDF |

No. of downloads: 218

Some examples of division symbol algebras of degree $3$ and $5$

Author: Cristina Flaut / Diana Savin

Abstract: In this paper we provide an algorithm to
compute the product between two elements in a symbol algebra of degree $n$
and we find an octonion algebra (in general, without division) in a
symbol algebra of degree three. Moreover, using MAGMA software, we will
provide some examples of division symbol algebras of degree $3$
and of degree $5$. PDF |

No. of downloads: 225

Uniform approximation of functions by Bernstein-Stancu operators

Author: Adrian Holhoș

Abstract: For the class of bounded and continuous functions on $(0,1)$ we give a characterization of the functions which can be uniformly approximated by Bernstein-Stancu operators. We also study the possibility of uniform approximation of unbounded functions by Bernstein-Stancu operators in weighted spaces with Jacobi weights. PDF |

No. of downloads: 183

Existence of three solutions for a three-point boundary value problem via a three-critical-point theorem

Author: Xiaojie Lin

Abstract: In this paper, we study the existence of at least three solutions
for a three-point boundary value problem. By constructing and
showing an appropriate separable and reflexive Banach space, a new multiplicity result of the three-point boundary value problem is established.
Our main tool is based upon variational method and three-critical-point
theorem. PDF |

No. of downloads: 191

Fixed point results for multivalued operators with respect to
a $c$-distance

Author: Enrique Llorens-Fuster / Cristina Urs

Abstract: In this paper we present a fixed point theorem for contractive type
multivalued operators in cone metric spaces by using the concept of
$c$-distance. PDF |

No. of downloads: 192

Ulam-Hyers-Rassias stability of pseudoparabolic partial differential equations

Author: Nicolaie Lungu / Sorina Anamaria Ciplea

Abstract: The aim of this paper is to give some types of Ulam stability for a pseudoparabolic partial
differential equation.
In this case we consider Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability.
We investigate some new applications of the Gronwall lemmas to the Ulam stability
of a nonlinear pseudoparabolic partial differential equations. PDF |

No. of downloads: 166

A new approach to fixed point theorems for multivalued contractive maps

Author: Gulhan Munak / Murat Olgun / Ishak Altun

Abstract: In the present paper, considering the Wardowski's technique we give many
fixed point results for multivalued maps on complete metric space without
using the Hausdorff metric. Our results are real generalization of some
related fixed point theorems including the famous Feng and Liu's result in
the literature. We also give some examples to both illustrate and show that
our results are proper generalizations of the mentioned theorems. PDF |

No. of downloads: 252

On some convergences to the constant $e$ and improvements of Carleman's inequality

Author: Cristinel Mortici / Hu Yue

Abstract: We present sharp inequalities related to the sequence $%
\left( 1+1/n\right) ^{n}$ and some applications to Kellers' limit and
Carleman's inequality. PDF |

No. of downloads: 197

Towards a new bound for a matrix norm

Author: P. G. Popescu / E. I. Sluțanschi / V. Preda

Abstract: In this paper are given refinements of several classical inequalities like Jensen, Young and Heinz which are then applied to obtain new improvements of recent results. We also give a new bound for a matrix norm expression, related to a matrix inequality of Bhatia and Davis. PDF |

Abstract: For an ordered subset $S = \{s_1, s_2,\dots s_k\}$ of vertices in a connected graph $G$, the metric representation of a vertex $u$ with respect to the set $S$ is the $k$-vector $ r(u|S)=(d_G(v,s_1), d_G(v,s_2),\dots,$ $d_G(v,s_k))$, where $d_G(x,y)$ represents the distance between the vertices $x$ and $y$. The set $S$ is a metric generator for $G$ if every two different vertices of $G$ have distinct metric representations with respect to $S$. A minimum metric generator is called a metric basis for $G$ and its cardinality, $dim(G)$, the metric dimension of $G$. It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae and tight bounds for the metric dimension of strong product graphs. PDF |