Geodesic
Subclasses of K-uniformly Convex and Starlike Functions Defined by Generalized Derivative, II
Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 91

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Recently, Kanas and Wiśniowska [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.
Classification : 30C45 33E05
Keywords: Convex functions, uniformly convex functions, $k$-uniformly convex functions, Jacobian elliptic functions 
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     author = {Stanis{\l}awa Kanas and Teruo Yaguchi},
     title = {Subclasses of {K-uniformly} {Convex} and {Starlike} {Functions} {Defined} by {Generalized} {Derivative,} {II}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {91 },
     publisher = {mathdoc},
     volume = {_N_S_69},
     number = {83},
     year = {2001},
     zbl = {1003.30010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a11/}
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Stanisława Kanas; Teruo Yaguchi. Subclasses of K-uniformly Convex and Starlike Functions Defined by Generalized Derivative, II. Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 91 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a11/