Volume 66 , issue 4 ( 2014 ) | back |

$\beta$-greedoids | 343$-$350 |

**Abstract**

In this paper, we introduce the notion of $\beta$-greedoids and discuss four basic constructions of $\beta$-greedoids namely, deletion, contraction, direct sum and ordered sum. We show that the operations of deletion and contraction commute and the direct sum and ordered sum of $\beta$-greedoids $G_{1}$ and $G_{2}$ are interval $\beta$-greedoids if and only if $G_{1}$ and $G_{2}$ are both interval $\beta$-greedoids. We also give a necessary and sufficient condition for the direct sum and ordered sum of balanced $\beta$-greedoids to be balanced.

**Keywords:** $\beta$-greedoid; basis; feasible; flat; density; direct sum; ordered sum.

**MSC:** 52C99

Fixed point for fuzzy contraction mappings satisfying an implicit relation | 351$-$356 |

**Abstract**

We prove a common fixed point theorem for generalized fuzzy contraction mappings satisfying an implicit relation.

**Keywords:** Fuzzy sets; fuzzy map; fuzzy contractive mappings; common fixed points.

**MSC:** 47H10, 54H25

A remark on the property $\mathcal P$ and periodic points of order $ınfty$ | 357$-$363 |

**Abstract**

In this paper, we considered the relationship between periodic points, fixed points, and the property $\mathcal P$. We also presented an extended version of periodic points together with their behaviors in topological spaces and cone metric spaces.

**Keywords:** Metric space; property $\mathcal P$; periodic point.

**MSC:** 47H09, 47H10

$n$-normal and $n$-quasinormal composition and weighted composition operators on $L^{2}(\mu)$ | 364$-$370 |

**Abstract**

An operator $T$ is called $n$-normal operator if $T^nT^* = T^*T^n$ and $n$-quasinormal operator if $T^nT^*T = T^*TT^n$. In this paper, the conditions under which composition operators and weighted composition operators become $n$-normal operators and $n$-quasinormal operators have been obtained in terms of Radon-Nikodym derivative $h_n$.

**Keywords:** normal operator; quasinormal operator; $n$-normal operator; $n$-quasinormal operator; composition operator; weighted composition operator;
conditional expectation operator; hyponormal operator; compact operator.

**MSC:** 47B20, 47B33, 47B38

Lightlike submanifolds of indefinite para-Sasakian manifolds | 371$-$386 |

**Abstract**

In this paper, we study invariant, slant and screen slant lightlike submanifolds of indefinite para-Sasakian manifolds. We obtain necessary and sufficient conditions for existence of slant and screen slant lightlike submanifolds of indefinite para-Sasakian manifolds and also provide non-trivial examples of such submanifolds. We obtain integrability conditions of distributions $D$ and $RadTM$ on screen slant lightlike submanifolds of indefinite para-Sasakian manifold. Further we obtain sufficient condition for induced connection on screen slant lightlike submanifolds of indefinite para-Sasakian manifold to be metric connection.

**Keywords:** Semi-Riemannian manifold; degenerate metric; radical distribution; screen distribution;
screen transversal vector bundle; Gauss and Weingarten formulae; totally geodesic and totally umbilical lightlike submanifold.

**MSC:** 53C15, 53C40, 53C50

Univariate fractional Polya type integral inequalities | 387$-$396 |

**Abstract**

Here we establish a series of various fractional Polya type integral inequalities with the help of generalized right and left fractional derivatives. We give an application to complex valued functions defined on the unit circle.

**Keywords:** Polya integral inequality; fractional derivative.

**MSC:** 26A33, 26D10, 26D15

Common fixed points of two multivalued nonexpansive maps by a one-step implicit algorithm in hyperbolic spaces | 397$-$409 |

**Abstract**

In this paper, we construct an implicit algorithm for two multivalued nonexpansive maps in a hyperbolic space and use it to approximate common fixed points of these maps through $\triangle$-convergence and strong convergence.

**Keywords:** Common fixed point; hyperbolic space; implicit algorithm; multivalued nonexpansive map; strong convergence; $\triangle$-convergence.

**MSC:** 47A06, 47H09, 47H10, 49M05

Results concerning symmetric generalized biderivations of prime and semiprime rings | 410$-$417 |

**Abstract**

The purpose of this paper is to prove some results concerning symmetric biderivations and symmetric generalized biderivations on prime and semiprime rings which partially extend some results contained in Vukman, J., Symmetric biderivations on prime and semiprime rings, Aequationes Math. 38 (1989), 245--254 and Vukman, J., Two results concerning symmetric biderivations on prime rings, Aequationes Math. 40 (1990), 181--189.

**Keywords:** Semiprime ring; generalized derivation; symmetric biderivation.

**MSC:** 16R50, 16W25, 16N60

Elliptic transmission problem in disjoint domains | 418$-$429 |

**Abstract**

In this paper, we investigate an elliptic transmission problem in disjoint domains. A priori estimate for its weak solution in appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a slowly increasing logarithmic factor of the mesh size), is obtained.

**Keywords:** Elliptic transmission problem; disjoint domains; Sobolev-like space.

**MSC:** 65N12, 65N15

Compact families and continuity of the inverse | 430$-$436 |

**Abstract**

We generalize a topological game introduced by Kenderov, Kortezov and Moors and use it to establish conditions under which a paratopological group is a topological group.

**Keywords:** Cover; filter; compact filter; topological group; paratopological group; topological game.

**MSC:** 54D30