a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...

A vertex v in a graph G dominates itself as well as its neighbors. A set S of vertices in G is (1) a dominating set if every vertex of G is dominated by some vertex of S, (2) an open dominating set if every vertex of G is dominated by a vertex of S distinct from itself, and (3) a double dominating set if every vertex of G is dominated by at least two distinct vertices of S. The minimum cardinal...

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

In this paper the phase-space of generic 2D area-preserving polynomial mappings is studied. These mappings modelize the transverse dynamics of a flat beam in a circular machine dominated by nonlinear magnetic errors. In particular, the problem of computing the dynamic aperture, i.e. the region in phase-space where stable motion occurs, is considered. The main result is that the boundary of the ...

Abstract The aim of this paper is to prove some new fixed point results for a pair multivalued dominated locally contractive mappings in b -multiplicative metric space. Further, theorems multigraph-dominated are also established. Some on closed ball obtained endowed with graphic structure An illustrative example given show the validity hypothesis our result. Moreover, applications coupled syste...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

Suppose that A and B are nonempty subsets of a complete metric space $$(\mathcal {M},d)$$ $$\phi ,\psi :A\rightarrow B$$ mappings. The aim this work is to investigate some conditions on $$ $$\psi such the two functions, one assigns each $$x\in A$$ exactly $$d(x,\phi x)$$ other $$d(x,\psi , attain global minimum value at same point in A. We have introduced notion proximally F-weakly dominated pa...

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.