Certain Bound for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Starlike and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Convex Functions with respect to Symmetric Points

Ramachandran, C.; Kavitha, D.; Soupramanien, T.

doi:10.1155/2015/205682

Cited by 14 publications

(11 citation statements)

References 11 publications

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“…The class T k α (ϕ) was introduced and studied by Parvatham and Radha [11] and this class generalizes the classes defined by Pascu [12], Das and Singh [5] as well as the classes S k s (ϕ) and C k s (ϕ) which were studied recently by Wang et al [18]. Recently several subclasses of analytic functions with respect to k-symmetric points were introduced and studied by various authors (see [1], [2], [14], [18], [19], [21]). Following Ma and Minda [7], Ravichandran et al [15] defined a more general class related to the class of starlike functions of complex order as follows.…”

Section: Introductionmentioning

confidence: 95%

Some properties for \(\alpha\)-starlike functions with respect to \(k\)-symmetric points of complex order

Darwish

Lashin

Sowileh

2017

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In the present work, we introduce the subclass \(\mathcal{T}_{\gamma ,\alpha<br />}^{k}(\varphi )\), of starlike functions with respect to \(k\)-symmetric points of complex order \(\gamma\) (\(\gamma \neq 0\)) in the open unit disc \(\vartriangle\). Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

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Section: Introductionmentioning

confidence: 95%

Some properties for \(\alpha\)-starlike functions with respect to \(k\)-symmetric points of complex order

Darwish

Lashin

Sowileh

2017

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“…Recently Uçar Özkan (see [8]) studied some properties of q -starlike and q -close to convex functions. Ramachandran [6] studied q -starlike and q -convex functions with respect to symmetric points. Polatoǧlu [5] investigated q−starlike functions and obtained growth and distortion theorems for this class.…”

Section: Introductionmentioning

confidence: 99%

Coefficient estimates for the class of quasi q-convex functions

Altıntaş¹,

Aydoğan²

2020

Turk J Math

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“…Recently, by Uçar et al [30], some properties of q−close-to-convex functions were studied. In [22], Ramachandran et al studied certain bound for q−starlike and q−convex functions with respect to symmetric points. In [22], the coefficient estimates for the subclasses of q−starlike and q−convex functions with respect to symmetric points involving q−difference operator were established and the authors provided certain applications based on these results for subclasses of univalent functions defined by convolution.…”

Section: Introductionmentioning

confidence: 99%