Volume 61 , issue 4 ( 2009 ) | back |

Some stability results for two hybrid fixed point iterative algorithms in normed linear space | 247$-$256 |

**Abstract**

In this paper, we prove some stability results for two newly introduced hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann Type in normed linear space using a certain contractive condition. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [29,30], Osilike [26], Berinde [2,3] as well as the recent results of the author [12,24,24,25].

**Keywords:** Kirk-Ishikawa iterative algorithms; Kirk-Mann iterative algorithms.

**MSC:** 47H06; 54H25

Stability and boundedness properties of solutions to certain fifth order nonlinear differential equations | 257$-$268 |

**Abstract**

In this paper, we consider the nonlinear fifth order differential equation $$x^{(v)}+ax^{(iv)}+b\dddot x+f(\ddot{x})+g(\dot{x})+h(x)=p(t; x, \dot{x},\ddot{x},\dddot x,x^{(iv)})$$ and we used the Lyapunov's second method to give sufficient criteria for the zero solution to be globally asymptotically stable as well as the uniform boundedness of all solutions with their derivatives.

**Keywords:** Boundedness; Lyapunov function; nonlinear fifth order differential equations; stability.

**MSC:** 34A34; 34D20, 34D23, 34D99

Some properties of Noor integral operator of $(n+p-1)$-th order | 269$-$279 |

**Abstract**

Let $A(p)$ be the class of functions $f(z)=z^{p}+\sum_{k=p+1}^{ınfty}a_{k}z^{k}$ $(pın N=\{1,2,\dots\})$ which are analytic in the unit disc $U=\{z:|z|<1\}$. The object of the present paper is to give some properties of Noor integral operator $I_{n+p-1}f(z)$ of $(n+p-1)$-th order, where $I_{n+p-1}f(z)=\left[ \frac{z^{p}}{(1-z)^{n+p}}\right]^{(-1)}*f(z)$ $(n>-p$, $f(z)ın A(p))$ and $*$ denotes convolution (Hadamard product).

**Keywords:** Analytic function; Noor integral operator; convolution.

**MSC:** 30C45

Subspace and addition theorems for extension and cohomological dimensions. A problem of Kuzminov | 281$-$305 |

**Abstract**

Let $K$ be either a CW or a metric simplicial complex. We find sufficient conditions for the subspace inequality $$A\subset X, \quad Kın \text{\rm AE}(X)\Rightarrow Kın \text{\rm AE}(A).$$ For the Lebesgue dimension ($K=S^n$) our result is a slight generalization of Engelking's theorem for a strongly hereditarily normal space $X$. As a corollary we get the inequality $$A\subset X\Rightarrow\dim_GA\leq\dim_GB.$$ for a certain class of paracompact spaces $X$ and an arbitrary abelian group $G$. As for the addition theorems $$\gather Kın \text{\rm AE}(A), \;\; Lın\text{\rm AE}(B)\Rightarrow K\ast Lın\text{\rm AE}(A\cup B),\\ \dim_G(A\cup B)\leq\dim_GA+\dim_GB+1, \endgather$$ we extend Dydak's theorems for metrizable spaces ($G$ is a ring with unity) to some classes of paracompact spaces.

**Keywords:** Dimension; cohomological dimension; absolute extensor; CW-complex; metric simplicial complex; subspace theorem; addition theorem.

**MSC:** 55M11; 54F45

Eightieth anniversary of the birth of Dušan Adnadjević | 307$-$310 |