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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, 35-959 Rzeszów, Poland and Department of Applied Mathematics, College of Humanities and Sciences, Nihon University, Sakurajousui, Setagaya, Tokyo 156-0045, 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
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Electronic fulltext finalized on: 5 Feb 2002.
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