Volume 63 , issue 3 ( 2011 )back
On sandwich theorems for some subclasses of analytic functions involving extended multiplier transformations157$-$169
M. K. Aouf, A. Shamandy, R. M. El-Ashwah and E. E. Ali

Abstract

In this paper we derive some subordination and superordination results for certain normalized analytic functions in the open unit disc, which are acted upon by a class of extended multiplier transformations. Relevant connections of the results, which are presented in this paper, with various known results are also considered.

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Keywords: Multiplier transformations; differential subordination; superordination.

MSC: 30C45

Comprehensive family of $k$-uniformly harmonic starlike functions171$-$180
B. A. Frasin and G. Murugusundaramoorthy

Abstract

In this paper, we introduce a comprehensive family of k-uniformly harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Coefficient bounds, distortion bounds, extreme points, convolution conditions, and convex combination are determined for functions in this family. Further results on integral transforms are discussed. Consequently, many of our results are either extensions or new approaches to those corresponding previously known results.

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Keywords: Harmonic function; analytic function; univalent function.

MSC: 30C45

Existence of mild solutions of a semilinear nonconvex differential inclusion with nonlocal conditions181$-$190
Myelkebir Aitalioubrahim

Abstract

We show two existence results of a mild solution for a semilinear nonconvex differential inclusion, with nonlocal condition, governed by a family of linear operators, not necessarily bounded or closed.

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Keywords: Evolution operator; differential inclusions; nonlocal conditions; mild solutions.

MSC: 34A60; 34B10, 34B15

Lambert multipliers of the range of composition operators191$-$199
M. R. Jabbarzadeh and S. Khalil Sarbaz

Abstract

In this note Lambert multipliers of the range of composition operators acting between different $L^p$ spaces are characterized by using some properties of conditional expectation operators. Also, necessary conditions for Fredholmness and normality of these type operators are investigated.

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Keywords: Conditional expectation; multipliers; multiplication operators; weighted composition operators.

MSC: 47B20; 47B38

Properties of new classes of multivalent analytic functions201$-$217
Jacek Dziok

Abstract

By means of the subordination, we introduce and investigate classes of multivalent functions with varying argument of coefficients and two fixed points. The results obtained here for each of these classes include coefficients estimates, growth and distortion theorems, radii of starlikeness and convexity, subordination theorems and integral means inequalities. Some consequences of the results for well-known classes of functions are also pointed out.

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Keywords: Analytic functions; varying arguments; fixed points; subordination; Hadamard product; integral means inequalities.

MSC: 30C45; 30C50, 30C55

A note on discretely absolutely star-Lindelöf spaces219$-$222
Yan-Kui Song

Abstract

In this paper, we prove the following statements: (1)~If $X$ is a normal discretely absolutely star-Lindel{ö}f space with $e(X)<\omega_1$, then the Alexandroff duplicate $A(X)$ of $X$ is discretely absolutely star-Lindel{ö}f. (2)~If $X$ is a space with $e(X)\geq\omega_1$, then $A(X)$ is not discretely absolutely star-Lindel{ö}f. The two statements answer a question raised by Song.

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Keywords: Star-Lindelöf; absolutely star-Lindelöf; discretely absolutely star-Lindelöf.

MSC: 54A25; 54D20

Numerical solutions of third kind integral-algebraic equations223$-$233
Azzeddine Bellour and E. A. Rawashdeh

Abstract

In this paper, collocation and discretized collocation methods for solving third kind integral-algebraic equations numerically are developed. The global convergence analysis using the spline polynomial space $S_{m-1}^{-1}(\Pi_{N})$ is given. We exhibit the methods and tabulate the results for several numerical test cases.

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Keywords: Third kind integral equations; collocation method.

MSC: 45D05; 65L60