On q-Calculus and Starlike Functions

Krzysztof Piejko1, Janusz Sokół2, Katarzyna Tra̧bka-Wiȩcław3
1Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland
2Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310, Rzeszów, Poland
3Mechanical Engineering Faculty, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618, Lublin, Poland

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Abu-Risha MH, Annaby MH, Ismail MEH, Mansour ZS (2007) Linear $$q$$-difference equations. Z Anal Anwend 26(4):481–494

Agrawal S, Sahoo SK (2014) Geometric properties of basic hypergeometric functions. J Differ Equ Appl 20:1502–1522

Agrawal S, Sahoo SK (2017) A generalization of starlike functions of order alpha. Hokkaido Math J 46:15–27

Annaby MH, Mansour ZS (2012) $$q$$-Fractional calculus and equations. Springer, Berlin

Aouf MK, Seoudy TM (2019) Convolution properties for classes of bounded analytic functions with complex order defined by $$q$$-derivative operator. Rev R Acad Cienc Exactas Fis Nat Ser A Mat, RACSAM 113:1279–1288

Ismail MEH, Merkes E, Styer D (1990) A generalization of starlike functions. Complex Var 14:77–84

Jackson FH (1908) On $$q$$-functions and certain difference operator. Trans R Soc Edinb 46:253–281

Jackson FH (1910) On $$q$$-definite integrals. Q J Pure Appl Math 41:193–203

Miller SS, Mocanu PT (2000) Differential subordinations theory and applications, series of monographs and textbooks in pure and applied mathematics, vol 225. Marcel Dekker Inc., New York

Mocanu PT (1986) On a theorem of Robertson. Babeş–Bolyai Univ Fac Math Res Sem Semin Geom Funct Theory 5:77–82

Piejko K, Sokół J On convolution and $$q$$-calculus, Boletin de la Sociedad M. Mexicana. (in print)

Raghavendar K, Swaminathan A (2012) Close-to-convexity of basic hypergeometric functions using their Taylor coefficients. J Math Appl 35:111–125

Robertson MS (1936) On the theory of univalent functions. Ann Math 37:374–408

Robertson MS (1985) Certain classes of starlike functions. Mich Math J 32:135–140

Rønning F (1994) A Szegö quadrature formula arising from $$q$$-starlike functions. In: Clement Cooper S, Thron WJ (eds) Continued fractions and orthogonal functions, theory and applications. Marcel Dekker Inc., New York, pp 345–352

Ruscheweyh ST, Sheil-Small T (1973) Hadamard product of schlicht functions and the Poyla–Schoenberg conjecture. Comment Math Helv 48:119–135

Sahoo SK, Sharma NL (2015) On a generalization of close-to-convex functions. Ann Pol Math 113:93–108

Seoudy TM, Aouf MK (2014) Convolution properties for certain classes of analytic functions defined by $$q$$-derivative operator. Abstr Appl Anal vol 2014, Article ID 846719, pp 1–7

Seoudy TM, Aouf MK (2016) Coefficient estimated of new classes of $$q$$-starlike and $$q$$-convex functions of complex order. J Math Inequal 10(1):135–145

Strrohhäcker E (1933) Beitrage zür theorie der schlichter functionen. Math Z 37:356–380

Wilken DR, Feng J (1980) A remark on convex and starlike functions. J Lond Math Soc 21(2):287–290