Certain Properties of Komatu Integral Transform with Negative Coefficients with Reference to Uniform Starlike and Uniform Convex Functions
R.Ambrose Prabhu1, S.Bhaskaran2, L.Vanitha3, R.Ravi Kumar4
Manuscript received on September 23, 2019. | Revised Manuscript received on October 15, 2019. | Manuscript published on October 30, 2019. | PP: 6816-6819 | Volume-9 Issue-1, October 2019 | Retrieval Number: A2982109119/2019©BEIESP | DOI: 10.35940/ijeat.A2982.109119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The authors obtained a new subclass about strongly starlike and strongly convex functions with respect to Komatu integral transforms and the inclusion properties of these classes such as 𝓢𝒑𝑻(𝝀,𝑰𝝂𝝆) and 𝓤𝓒𝓥𝓣(𝝀,𝑰𝝂𝝆) were discussed . Furthermore, a new subclass about uniformly starlike functions along uniformly convex functions including negative coefficients defined by the Komatu integral transforms are introduced. The various properties about these classes are obtained here including (for instance) coefficient estimates, extreme points, distortion and covering theorems. Mathematics Subject Classification: Primary 30C45.
Keywords: Univalent function, Komatu integral transforms, starlike function and extreme points.