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TitleRemarks on Metric-Type Spaces and Applications
Vol.39(6) (2015) page: 755--768
Author(s): N.V. Dung, V.T.L. Hang and S. Sedghi  

In this paper, we prove some properties of metric-type spaces. As applications, we show that fixed point theorems on bounded 2-metric spaces and S-metric spaces in [18,22] and others may be obtained from certain fixed point theorems on metric-type spaces.

Keywords: Metric spaces; Cauchy Sequences; Weak Metric-type space.
Size:126KB   download
TitleSome Characterizations of 2-primal Ternary Semiring
Vol.39(6) (2015) page: 769--783
Author(s): T.K. Dutta and S. Mandal  

In this paper we introduce the notion of 2-primal ternary semiring.Also we define symmetric ternary semiring, NI ternary semiring and NCI ternary semiring. Properties of 2-primal ternary semirings are established.

Keywords: Strongly nilpotent; Super nilpotent; 2-primal; Strongly regular ternary semiring; NI ternary semiring; NCI ternary semiring and (S I) ternary semiring.
Size:156KB   download
TitleTopological Robotics and Hyperplane Arrangements
Vol.39(6) (2015) page: 785--797
Author(s): M. Jambu  

This paper is a short survey of some results on topological robotics. M. Farber introduced the notion of topological complexity [1, 2, 3] which is an important homotopy invariant closely related to the instability of mechanical systems.

In a first part, following M. Farber, we recall the definition and properties of the configuration spaces of a mechanical system, of the topological complexity as well as instability of the system. Then, in the second part, we focus on some configuration spaces, the complements of hyperplane arrangements. We recall some results obtained by M. Farber and S. Yuzvinski [4] and we extend these results to the fiber-type arrangements.

Keywords: Motion planning; Topological complexity; Hyperplane arrangements.
Size:151KB   download
TitleDynamic Betting Game
Vol.39(6) (2015) page: 799--814
Author(s): C.J. Lien  

Players A and B play a betting game. Player A starts with initial money n. In each of k rounds, player A can wager an integer w between 0 and what he has currently. B then decides whether A wins or loses. If A wins, he receives w money, and if A loses, he loses w money. A total of k rounds are played, but A can only lose r times. What strategy should A use to end with the maximum amount of money, D(n, k, r)?

In this paper, we provide a strategy for A to maximize his money and the algorithm to calculate D(n, k, r). We study the periodicity of D(n+1, k, r)−D(n, k, r) relative to n. We will also extend n and w to non-negative real numbers. The maximum amount of money that A can obtain with continuous money is C(n, k, r), and we study the relationship between C and D.

Keywords: Betting game; Dynamic game; Zero-sum game.
Size:166KB   download
TitleCayley Digraphs of Brandt Semigroups Relative to Green's Equivalence Classes
Vol.39(6) (2015) page: 815--827
Author(s): J. Meksawang and S. Panma  

This paper we describe Cayley digraph of Brandt semigroups relative to Green's equivalence classes. Moreover, we investigate isomorphic conditions for those Cayley digraphs.

Keywords: Cayley digraph; Digraph; Brandt semigroup; Right group; Rectangular group.
Size:149KB   download
TitleGoodman-Rønning-Type Multivalent Harmonic Functions Based on Dziok-Srivastava Operator
Vol.39(6) (2015) page: 829--840
Author(s): A.O. Mostafa and M.K. Aouf  

In this paper, a class of Goodman-Rønning-type multivalent harmonic functions based on Dziok-Srivastava operator is considered. Coefficient bounds, representation theorem, distortion and extreme points for functions of this class are obtained.

Keywords: Goodman-Rønning-type; Multivalent; Harmonic functions; Distortion; Extreme points.
Size:137KB   download
TitlePrime O-Ideals in Almost Distributive Lattices
Vol.39(6) (2015) page: 841--850
Author(s): N. Rafi, R.K. Bandaru and G.C. Rao  

In this paper we derive some sufficient conditions for a prime ideal of an Almost Distributive Lattice to become an O-ideal. A set of equivalent conditions are established for every O-ideal to become an annihilator ideal. An equivalency is obtained between prime O-ideals and minimal prime ideals of an ADL. Finally, obtained that any two distinct prime O-ideals of an ADL are co-maximal.

Keywords: Prime O-ideal; Filter; Annihilator ideal; ∗−ADL; Co-maximality.
Size:122KB   download
TitleSecond-Order Differential Superordination for Analytic Functions With Fixed Initial Coefficient
Vol.39(6) (2015) page: 851--864
Author(s): R. Mendiratta, S. Nagpal and V. Ravichandran  

Appropriate modifications are made to the theory of second order differential superordination developed by Miller and Mocanu to investigate the analytic functions in the unit disk \mathbbD with fixed initial coefficient; in particular, a suitable class Φβ of functions is determined for which the following implication is satisfied:

φ ∈ Φβ    and    Ω ⊂ {φ(p(z),zp′(z),z2p"(z);z):z ∈ \mathbbD}    ⇒     ∆ ⊂ p(\mathbbD),

where Ω and ∆ are sets in \mathbbC, φ(r,s,t;z):\mathbbC3×\mathbbD→\mathbbC and p is analytic in \mathbbD with fixed initial coefficient β. Several interesting examples are also provided.

Keywords: Differential superordination; Fixed initial coefficient; Univalent functions.
Size:155KB   download
TitleThe Space of Prime Ordered Filters of Heyting Almost Distributive Lattices
Vol.39(6) (2015) page: 865--875
Author(s): M. Sambasiva Rao and G.C. Rao  

The Stone's theorem of prime filters is generalized to the case of prime ordered filters of Heyting almost distributive lattices. Some topological properties of prime ordered filters are studied. Some equivalent conditions are derived for the space of prime ordered filters to become a Hausdorff space.

Keywords: Heyting ADL; Ordered filter; Compact set; Hausdorff space.
Size:116KB   download
TitleCertain Subclass of p-valent Functions Defined by the Generalized Integral Operator
Vol.39(6) (2015) page: 877--890
Author(s): T.M. Seoudy  

In the present paper, we investigate several inclusion relationships and other interesting properties of certain subclasses of multivalent functions which are defined here by means of generalized integral operator. Some of our results improve and generalize previously known results.

Keywords: Analytic function; Linear operator; Hadamard product; Subordination.
Size:149KB   download
TitleSome Properties of Regular Monoids
Vol.39(6) (2015) page: 891--902
Author(s): V.K. Sreeja and A.R. Rajan   

A monoid S with group of units G is said to be regular if for each x ∈ S, there is an element a ∈ S such that x = xax. We consider arbitrary monoids and describe various properties depending on the group of units. Properties of regular monoids and description of some special classes of regular monoids are also given.

Keywords: Coset; Greens equivalence; Unit regular inverse monoid; R(L) strongly unit regular; E centralising.
Size:132KB   download
TitleContents for Volume 39
Vol.39(6) (2015) page: 903--906
Size:50KB   download
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