CONVOLUTION PROPERTIES FOR CERTAIN SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS BY MEANS OF CASSINIAN OVALS
Abstract
In the present paper we introduce two new sub-categories MS∗q,η(p, s; d) and MK q,η(p, s; d) for a variety of meromorphic operations using a q-derivative operator defined on a perforated unit disk. We use Cassinian Oval √1 + dz with d ∈ (0, 1] as a subordinant function. We also find the necessary and sufficient conditions for the activities of these clauses.
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bibitem{21} {sc S. Agrawal {rm and} S.K. Sahoo}: {it A generalization of starlike functions of order $alpha$}. { Hokkaido Math. J.} textbf{46} (2017), 15-27.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{mkaouf} {sc M.K. Aouf, sc J. Dziok {rm and} sc J. Sokol}: {it On a subclass of strongly starlike functions.}
{Appl. Math. Letters.} {bf24} (2011), 27-32.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{veeru} {sc N.E. Cho, sc V. Kumar, sc O.S. Kwon {rm and} sc Y.J. Sim}: {it Coefficient bounds for certain subclasses of starlike functions}.{ J. Inequal. Appl.} 276 (2019) 13 pages. doi.org/10.1186/s13660-019-2231-3.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{3} { sc G. Gasper {rm and} sc M. Rahman}: {it Basic Hypergeometric Series}. { Cambridge University Press, Cambridge}, 1990.
%%%%%%%%%%%%%%%%%%%%%
bibitem{5} {sc F.H. Jackson}: {it On $q$-functions and a certain difference operator}. Trans. R. Soc. Edinb. textbf{46(2)} (1909), 253-281.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{6} {sc F.H. Jackson}: {it On $q$-definite integrals}. { Quart. J. Pure Appl. Math.} textbf{41} (1910), 193-203.
%%%%%%%%%%%%%%%%%%%%
bibitem{7}{sc F.H. Jackson}: {it $q$-difference equations}. {Amer. J. Math.} textbf{32} (1910), 305-314.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{1} {sc S.D. Purohit {rm and} R.K. Raina}: {it Certain subclasses of analytic functions associated with fractional $q$-calculus operators}. { Math. Scand.} textbf{109(1)} (2011), 55-70.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{rahim} {sc R. Kargar {rm and} sc L. Trojnar-Spelina}: {it Some applications of differential subordination for certain starlike functions}. { arXiv.org, math, arXiv:1807.03328}.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{nicz} {sc E. Niczyporowicz}: {it Krzywe plaskie.} { PWN, Warszawa}, 1991.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{17} {sc T.M. Seoudy}: {it Classes of analytic functions associated with certain integral operator}. { Electron. J. Math. Anal. Appl.} textbf{4(2)} (2016), 254-258.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{16} {sc T.M. Seoudy {rm and} sc M.K. Aouf}: {it Convolution properties for certain classes of analytic functions
defined by $q$-derivative operator}. { Abstr. Appl. Anal.} (2014), 7 pages, Article ID 846719.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{19}{sc H. Shamsan {rm and} sc S. Latha}: {it On generalized bounded mocanu variation related to $q$-derivative and conic regions}. { Annals of Pure and Applied Mathematics}. textbf{17(1)} (2018), 67-83.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{sokol} {sc J. Sokol}: {it Coefficient estimates in a class of strongly starlike functions.} { Kyungpook Math. J.}. {bf49} (2009), 349-353.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{20} {sc H.M. Srivastava}: {it Operators of basic (or $q$-) calculus and fractional $q$-calculus and their applications in geometric function theory of complex analysis}. { Iran. J. Sci. Technol. Trans. A Sci.} textbf{44(1)} (2020), 327-344.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{18} {sc H.M. Srivastava {rm and} sc D. Bansal}: {it Close-to-convexity of a certain family of $q$-Mittag-Leffler functions}. { J. Nonlinear Var. Anal.} textbf{1} ;(2017), 61-69.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{2} {sc R. Srivastava {rm and} H.M. Zayed}: {it Subclasses of analytic functions of complex order defined by $q$-derivative operator}. { Stud. Univ. Babec{s}-Bolyai Math.} textbf{64(1)} (2019), 71-80.
%%%%%%%%%%%%%%%%%%%%%%
bibitem{naya} {sc Y. Yunus, sc A.B. Akbarally {rm and} sc S.A. Halim}:
{it On a subclass of starlike functions associated with generalized cardioid}. { Int. J. Appl. Math.} {bf33(5)} (2020), 765-782.
%%%%%%%%%%%%%%%%%%%%%%%
bibitem{22} {sc H.M. Zayed {rm and} sc M.K. Aouf}: {it Subclasses of analytic functions of complex order associated with $q$-Mittag Leffler function}. { J. Egyptian Math. Soc.}. textbf{26(2)} (2018), 278-286.
DOI: https://doi.org/10.22190/FUMI220404002S
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