Close-to-Convexity of Convolutions of Classes of Harmonic Functions
For j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmon...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/3808513 |
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| author | Raj Kumar Garg Jay M. Jahangiri |
| author_facet | Raj Kumar Garg Jay M. Jahangiri |
| author_sort | Raj Kumar Garg |
| collection | DOAJ |
| description | For j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmonic in z<1. |
| format | Article |
| id | doaj-art-76b26378eda44a3f8bd74265e4793c1c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-76b26378eda44a3f8bd74265e4793c1c2025-02-03T01:32:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/38085133808513Close-to-Convexity of Convolutions of Classes of Harmonic FunctionsRaj Kumar Garg0Jay M. Jahangiri1DAV University, Jalandhar, Punjab 144012, IndiaMathematical Sciences, Kent State University, Burton, OH 44021-9500, USAFor j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmonic in z<1.http://dx.doi.org/10.1155/2018/3808513 |
| spellingShingle | Raj Kumar Garg Jay M. Jahangiri Close-to-Convexity of Convolutions of Classes of Harmonic Functions International Journal of Mathematics and Mathematical Sciences |
| title | Close-to-Convexity of Convolutions of Classes of Harmonic Functions |
| title_full | Close-to-Convexity of Convolutions of Classes of Harmonic Functions |
| title_fullStr | Close-to-Convexity of Convolutions of Classes of Harmonic Functions |
| title_full_unstemmed | Close-to-Convexity of Convolutions of Classes of Harmonic Functions |
| title_short | Close-to-Convexity of Convolutions of Classes of Harmonic Functions |
| title_sort | close to convexity of convolutions of classes of harmonic functions |
| url | http://dx.doi.org/10.1155/2018/3808513 |
| work_keys_str_mv | AT rajkumargarg closetoconvexityofconvolutionsofclassesofharmonicfunctions AT jaymjahangiri closetoconvexityofconvolutionsofclassesofharmonicfunctions |