Editor in Chief - Anry Nersessian (Institute of Mathematics NAS, Armenia)
Deputy Editor - Rafayel Barkhudaryan (Institute of Mathematics NAS, Armenia)
Managing Editor - Linda Khachatryan (Institute of Mathematics NAS, Armenia)
e-mail: ajm@instmath.sci.am
According to the latest Scimago Journal Rank, Armenian Journal of Mathematics has maintained its position in Q3 with an SJR score of 0.36.
Read more about Armenian Journal of Mathematics has been recognized as a Q3 journal in SJRIn this paper, we examine the geometric properties of linear operators associated with normalized Jackson and Hahn-Exton $q$-Bessel functions that arise through suitable transformations and $q$-extension of the Hohlov integral operator. These operators are investigated in the framework of the function from the class $\mathcal{M}_{\xi,\varkappa}^{\varpi,\theta}(z;q)$. We derive coefficient bounds and sufficient conditions for functions in the class $\mathcal{M}_{\xi,\varkappa}^{\varpi,\theta}(z;q)$. Additionally, we explore inclusion properties by using the Taylor coefficients of $z_2\phi_1(a,b;c;q,z)$ and the normalized Jackson and Hahn-Exton $q$-Bessel functions. The primary objective is to derive sufficient conditions under which the convolution operators will be in different subclasses of $q$-starlike and $q$-convex functions.
L.D. Abreu, A q-sampling theorem related to the q-Hankel transform. Proc. Amer. Math. Soc., 133 (2005), no. 4, pp. 1197-1203.
S. Agrawal and S.K. Sahoo, A generalization of starlike functions of order α. Hokkaido Math. J., 46 (2017), pp. 15-27.
I. Aktas and Á. Baricz, Bounds for radii of starlikeness of some q-Bessel functions. Results Math., 72 (2017), pp. 947-963.
G.E. Andrews, R. Askey and R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
M.H. Annaby, Z.S. Mansour and O.A. Ashour, Sampling theorems associated with biorthogonal q-Bessel functions. J. Phys. A, 43 (2010), no. 29, 295204.
R. Askey, The q-Gamma and q-Beta functions. Appl. Anal., 8 (1978), pp. 125-141.
Á. Baricz, Geometric properties of generalized Bessel functions. Publ. Math. Debrecen, 73 (2008), no. 11, pp. 155-178.
Á. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Math., vol. 1994, Springer-Verlag, Berlin, 2010.
Á. Baricz, D.K. Dimitrov and I. Mezö, Radii of starlikeness and convexity of some q-Bessel functions. J. Math. Anal. Appl., 435 (2016), no. 1, pp. 968-985.
Á. Baricz and R. Szász, The radius of convexity of normalized Bessel functions of the first kind. Anal. Appl., 12 (2014), no. 5, pp. 485-509.
Á. Baricz and R. Szász, Close-to-convexity of some special functions and their derivatives. Bull. Malays. Math. Sci. Soc., 39 (2016), pp. 427-437.
R.K. Brown, Univalence of Bessel functions. Proc. Amer. Math. Soc., 11 (1960), pp. 278-283.
J.L. Cardoso, On basic Fourier-Bessel expansions, SIGMA, 14 (2018), no. 35, 13 pp.
A.B.O. Daalhuis, Asymptotic expansions for q-gamma, q-exponential and q-Bessel functions, J. Math. Anal. Appl., 186 (1994), no. 3, pp. 896-913.
G. Dattoli and A. Torre, q-Bessel functions: The point of view of the generating function method. Rend. Mat. Appl., 17 (1997), pp. 329-345.
P.L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 2004.
M.K. Giri and R. Kondooru, Exploring the inclusion properties of integral operators related to the Pascal distribution series in certain subclasses of univalent functions. Sahand Commun. Math. Anal., 22 (2025), no. 2, pp. 261-289.
M.K. Giri and K. Raghavendar, Inclusion results on hypergeometric functions in a class of analytic functions associated with linear operators. Contemp. Math., 5 (2024), no. 2, pp. 2315-2334.
M.E.H. Ismail, E. Merkes and D. Styer, A generalization of starlike functions. Complex Variables, 14 (1990), pp. 77-84.
M.E.H. Ismail and M.E. Muldoon, On the variation with respect to a parameter of zeros of Bessel and q-Bessel functions. J. Math. Anal. Appl., 135 (1988), no. 1, pp. 187-207.
F.H. Jackson, On q-definite integrals. Quart. J. Pure Appl. Math., 41 (1910), pp. 193-203.
F.H. Jackson, q-difference equations. Amer. J. Math., 32 (1910), pp. 305-314.
W. Janowski, Some extremal problems for certain families of analytic functions I. Ann. Pol. Math., 28 (1973), pp. 297-326.
H.T. Koelink and R.F. Swarttouw, On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials. J. Math. Anal. Appl., 186 (1994), pp. 690-710.
T.H. Koornwinder and R.F. Swarttouw, On q-analogues of the Hankel and Fourier transforms. Trans. Amer. Math. Soc., 333 (1992), pp. 445-461.
S.R. Mondal, M.K. Giri and R. Kondooru, Sufficient conditions for linear operators related to confluent hypergeometric function and generalized Bessel function of the first kind to belong to a certain class of analytic functions. Symmetry, 16 (2024), no. 6, 662.
S.R. Mondal, M.K. Giri and R. Kondooru, Results on linear operators associated with Pascal distribution series for a certain class of normalized analytic functions. Mathematics, 13 (2025), no. 7, pp. 115-128.
K. Raghavendar and A. Swaminathan, Integral transforms of functions to be in certain class defined by the combination of starlike and convex functions. Comput. Math. Appl., 63 (2012), no. 8, pp. 1296-1304.
E.D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
T.M. Seoudy and M.K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order. J. Math. Inequal, 10 (2016), no. 1, pp. 135-145.
H.M. Srivastava, B. Khan, N. Khan and Q.Z. Ahmad, Coefficient inequalities for q-starlike functions associated with the Janowski functions. Hokkaido Math. J., 48 (2019), no. 2, pp. 407-425.
H.M. Srivastava, M. Tahir, B. Khan, Q.Z. Ahmad and N. Khan, Some general families of q-starlike functions associated with the Janowski functions, Filomat, 33 (2019), no. 9, pp. 2613-2626.
G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944.
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