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SUBCLASSES OF $k$UNIFORMLY CONVEX AND STARLIKE FUNCTIONS DEFINED BY GENERALIZED DERIVATIVE, II
Stanis\l awa Kanas and Teruo Yaguchi
Department of Mathematics, Rzeszów University of Technology, 35959 Rzeszów, Poland and Department of Applied Mathematics, College of Humanities and Sciences, Nihon University, Sakurajousui, Setagaya, Tokyo 1560045, Japan
Abstract: Recently, Kanas and Wi\'sniowska [7, 8, 9] introduced the class of $k$uniformly convex, and related class of $k$starlike functions ($0 \le k < \infty$), denoted $\ku$ and $\ks$, respectively. In the present paper a notion of generalized convexity, by applying the well known Ruscheweyh derivative, is introduced. Some extremal problems for functions satisfying the condition of generalized convexity are solved.
Keywords: Convex functions, uniformly convex functions, $k$uniformly convex functions, Jacobian elliptic functions
Classification (MSC2000): 30C45; 33E05 Full text of the article:
Electronic fulltext finalized on: 5 Feb 2002.
This page was last modified: 5 Feb 2002.
© 2002 Mathematical Institute of the Serbian Academy of Science and Arts
© 2002 ELibM for
the EMIS Electronic Edition
