Volume 60 , issue 2 ( 2008 )back
Abstract formulation of an age-physiology dependent population dynamics problem79$-$86
Jean M. Tchuenche

Abstract

We transform a population dynamics problem with an additional structure into an abstract Cauchy problem, and use functional analytic method to solve it. Instead of using the familiar theory of resolvent, we rather replace the condition of well-posedness by its equivalent form in order to prove the existence of a unique weak solution. An {ıt a priori} estimate of the solution is also given as well as the perturbation about the equilibrium point, and by a bounded linear operator.

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Keywords: Population dynamics, age dependent, physiology, semigroup, linear/positive operator.

MSC: 35B45, 47B65, 47D06, 47H20.

On a class of multivalent functions defined by a multiplier transformation87$-$94
Sukhwinder Singh, Sushma Gupta and Sukhjit Singh

Abstract

In the present paper, the authors investigate starlikeness and convexity of a class of multivalent functions defined by multiplier transfomation. As a consequence, a number of sufficient conditions for starlikeness and convexity of analytic functions are also obtained.

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Keywords: Multivalent function; starlike function; convex function; multiplier transformation.

MSC: 30C45

On quasi almost lacunary strong convergence difference sequence spaces defined by a sequence of moduli95$-$100
Vakeel A. Khan and Q. M. Danish Lohani

Abstract

The idea of difference sequence sets, $X(\triangle)=\{\,x=(x_k):\triangle xın X\,\}$, where $X=l_ınfty$, $c$ or $c_0$ was introduced by Kizmaz [3], and then this subject has been studied and generalized by various mathematicians. In this article we define quasi almost $\triangle^m$-Lacunary strongly P-convergent sequences defined by sequence of moduli and give inclusion relations on these sequence spaces.

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Keywords: Difference sequence; lacunary sequence; sequence of moduli; double sequence.

MSC: 40C05, 42B15

Weakly contractive maps and common fixed points101$-$106
Akbar Azam and Muhammad Shakeel

Abstract

We prove the existence of common coincidence point and common fixed point for the self mappings satisfying a generalized weak contractive condition. Consequently it is shown that sequence of Mann type iterations associated with two self-mappings on convex metric space converges to their common fixed point.

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Keywords: Common fixed point; coincidence point; weakly contractive mappings; convex metric space.

MSC: 47H10, 54H25

An iterative method for variational inequality problems and fixed point problems in Hilbert spaces107$-$120
Xiaolong Qin, Meijuan Shang and Yongfu Su

Abstract

In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a relaxed $(\gamma,r)$-cocoercive, Lipschitz continuous mapping. Our results improve and extend the corresponding results of many others.

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Keywords: Projection method; relaxed cocoercive mapping; nonexpansive mapping; fixed point.

MSC: 47H05, 47H09; 47J05; 47J25

Uniqueness of meromorphic functions sharing a small function with their derivatives121$-$135
Abhijit Banerjee

Abstract

Using the notion of weakly weighted sharing we prove two uniqueness theorems concerning meromorphic functions sharing a small function with their derivatives, the first of which will improve all the results recently obtained by Lin-Lin [7] and thus provide a better answer to the questions posed by Yu [11] in this regard. Also with the aid of a recently introduced sharing notion in [1] known as relaxed weighted sharing we supplement one recent result of Lin-Lin~[7].

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Keywords: Meromorphic function; derivative; small function; weakly weighted sharing.

MSC: 30D35

Boundedness in topological spaces137$-$148
Giuseppe Di Maio and Ljubiša D. R. Kočinac

Abstract

We investigate abstract boundedness in a topological space and demonstrate the importance of this notion in selection principles theory. Some applications to function spaces and hyperspaces are given. This approach sheds more light on several results scattered in the literature.

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Keywords: Boundedness, $\Bbb B$-cover, $\gamma_{\Bbb B}$-cover, selection principles, topological games, partition symbol, countable fan tightness, countable strong fan tightness, $T$-tightness, $C_b(X)$, hyperspaces.

MSC: 54A25, 54B20, 54C35, 54D20, 03E02, 91A44.

Convergence of the Ishikawa iterate for multi-valued mappings in metric spaces of hyperbolic type149$-$154
Ljubomir B. Ćirić and Nebojša T. Nikolić

Abstract

Let ($X,d)$ be a metric spaces of hyperbolic type, $C$ be a closed and of hyperbolic type subset of $X$ and let $B(C)$ be the family of all nonempty bounded subsets of $C$. In this paper some results on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings $S,T\:C\to B(C)$ which satisfy the condition (2.1) below, are obtained.

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Keywords: Multi-valued mappings; Ishikawa iterate; spaces of hyperbolic type.

MSC: 54H25, 47H10