A Note on q–Calculus

Open access


In this article, we let PCq denote the class of q-convex functions. Certain analytic properties of the class PCq are studied. The maximum of the absolute value of the Fekete-Szegö functional is briey determined.

[1] Abdel-Gawad H.R., Thomas D.K., Fekete-Szegö problem for strongly close-to-convex function, Proc. Amer. Math. Soc., 114(1992), 345-249.

[2] Agrawal S., Sahoo S.K., A generalization of starlike functions of order alpha, arXiv.1404.3988, 2014(2014), 14 pages.

[3] Aldweby H., Darus M., Properties of a subclass of analytic functions defined by generalized operator involving q-hypergeometric functions, Far East J. Math. Sc., 81(2)(2013), 189-200.

[4] Aldweby H., Darus M., Some subordination results on q-analogue of Ruscheweyh differential operator, Abstract and Applied Analysis, 2014(2014), Article ID 958563, 6 pages.

[5] Ezeafulukwe U.A., Darus M., Certain properties of q-hypergeometric functions, Inter. J. Math. Math., 2015( 2015), Article ID 489218, 9 pages.

[6] Fekete M., Szegö G.,, Eine bemerkungüber ungerade schlichte funktionen, J. London Math. Soc., 8(1933), 85-89.

[7] Frasin B., Darus M., On Fekete-Szegö problem using Hadamard product, Int. J. Math. Math. Sci., 12(2003), 1289-1295.

[8] Ismail M.E.H., Merkes E., Styer D., A generalization of starlike functions, Complex Variables Theory Appl., 14(1990), 77-84.

[9] Jackson F.H., On q-difference integrals, Quart. J. Pure and Appl., 41(1910), 193-203.

[10] Jackson F.H., On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46(1909), 253-281.

[11] Jackson F.H., q-difference equations, Amer. J. of Math., 32(1910), 305-314.

[12] Keogh F.R., Merkes E.P., A coeficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20(1969), 8-12.

[13] Merkes E., Scott W., Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12(1961), 885-888.

[14] Mohammed A., Darus M., A generalized operator involving the q-hypergeometric functions, Matematicki Vesnik, 65(2013), 454-465.

[15] Nehari Z., Conformal Mapping, Mariner, Tampa, Fla, USA, 1952.

[16] Pommerenke Ch., Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.

[17] Raghavendar K., Swaminathan A., Close-to-convexity of basic hypergeometric functions using their Taylor coeficients, J. Math. Appl., 35(2012), 111-125.

[18] Sahoo S.K., Sharma N.L., On a generalization of close-to-convex functions, Ann. Polonici Math., 113(2015), 108-205.

[19] Selvakumaran K.A., Purohit S.D., Secer A., Majorization for a class of analytic functions defined by q-differentiation, Math. Problems Eng., 2014(2014), 5 pages.

[20] Sofonea D.F., Some new properties in q-calculusI , Gen. Math. , 16(2008), 47-54.

[21] Srivastava H.M., Owa S., Univalent Functions, Fractional calculus, and Their Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1989.

Journal Information

Mathematical Citation Quotient (MCQ) 2017: 0.08

Target Group

researchers in the fields of pure mathematics


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 272 264 19
PDF Downloads 106 103 6