Fekete-Szego problem for certain analytic functions defined by q−derivative operator with respect to symmetric and conjugate points.
ResumenRecently, the q−derivative operator has been used to investigate several subclasses of analytic functions in different ways with different perspectives by many researchers and their interesting results are too voluminous to discuss. For example, the extension of the theory of univalent functions can be used to describe the theory of q−calculus, q−calculus operator are also used to construct several subclasses of analytic functions and so on. In this work, we considered the FeketeSzego problem for certain analytic functions defined by q−derivative operator with respect to symmetric and conjugate points. The early few coefficient bounds were obtained to derive our results.
R.M. Ali, S.K. Lee, V. Ravichandran and S. Supramaniam, The Fekete-Szego coefficient functional for transforms of analytic functions, Bulletin of the Iranian Mathematical Society, 35 (2), pp. 119-142, (2009).
A. Aral, V. Gupta and R.P. Agarwal, Applications of q-Calculus in Operator Theory, Springer-Verlag, New York, (2013).
A.M. Gbolagade, S.O. Olatunji and T. Anake, Coefficient bounds for certain classes of analytic and univalent functions as related to sigmoid function, International Electronic Journal of Pure and Applied Mathematics, 7 (1), pp. 41-51, (2014).
R.M. Goel and B.C. Mehrok, A subclass of starlike functions with respect to symmetric points, Tamkang Journal of Mathematics, 13 (1), pp. 11-24, (1982).
S. Hussain, M.A. Alamri and M. Darus On a new class of (j, i)−symmetric function on conic regions, Journal of Nonlinear Sciences and Applications, 10, pp. 4628-4637, (2017).
F. H. Jackson, On q-definite integrals, The Quarterly Journal of Pure and Applied Mathematics, 28, pp. 193-203, (1910).
F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46, pp. 253-281, (1908).
J.M. Jahangiri, C. Ramachandran and S. Annamalai, Fekete-Szego problem for certain analytic functions defined by hypergeometric functions and Jacobi Polynomial, Journal of Fractional Calculus and Applications, 9 (1), pp. 1-7, (2018).
S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, continued fractions and geometric function theory (CONFUN), Trondheim, (1997) Journal of Computational and Applied Mathematics, 105, pp. 327-336, (1999).
S. Kanas and A. Wisniowska, Conic domains and starlike functions, Revue Roumaine des Mathematiques Pures et Appliquees, 45, pp. 645-658, (2000).
N. Magesh, S. Altinkaya and S. Yalcin, Construction of Toeplitz matrices whose elements are coefficient of univalent functions associated with q-derivative operator, arxiv: 1708.03600v1 (2017).
N. Magesh, S. Altinkaya and S. Yalcin, Certain subclases of k−uniformly starlike functions associated with symmetric q−derivative operator, Journal of Computational Analysis and Applications, 24 (8), pp. 1464-1473, (2018).
S.D. Purohit and R.K. Raina, Fractional q-calculus and certain subclases of univalent analytic functions, Mathematica, 55(78) (1), pp. 62-74, (2013).
C. Selvaraj and N. Vasanthi, Subclasses of analytic functions with respect to symmetric and conjugate points, Tamkang Journal of Mathematics , 13 (1), pp. 11-24, (1982).