Fekete-Szegö Inequality for (𝒑,𝒒)-Starlike and (𝒑,𝒒)-Convex Functions of Complex Order

Year 2020, Volume: 10 Issue: 2, 1247 - 1253, 01.06.2020

Feyza Yatkın Ekrem Kadıoğlu

https://doi.org/10.21597/jist.686462

Abstract

We have investigated Fekete-Szegö inequality in the classes of (𝑝,𝑞)-starlike and (𝑝,𝑞)-convex functions of complex order defined in the disc 𝑈={𝑧∈ℂ:|𝑧|<1}. Our main theorems are also a generalization of the result obtained.

Keywords

Fekete-Szegö İnequality , (𝑝 , Starlike Functions , Convex Functions , Complex Order

References

• Acar T, Aral A, Mohiuddine SA, 2016. On Kantorovich modification of (p, q)-Baskakov operators. J. Inequal. Appl. 13 pages. DOI: http://dx.doi.org/10.1186/s13660-016-1045-9.
• Cetinkaya A, Kahramaner Y, Polatoglu Y, 2018. Fekete-Szegö inequalities for q-starlike and q-convex functions. Acta Univ. Apulensis (53): 55-64.
• Chakrabarti R, Jagannathan R, 1991. A (p,q)-oscillator realization of two-parameter quantum algebras. J. Phys. A: Math. Gen. 24(13): 711-718.
• Jackson FH, 1908. On q-functions and a certain difference operator. Trans. Royal Soc. Edinburgh. (46): 253-281.
• Jagannathan R, Rao KS, 2006. Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series. arXiv:math/0602613v1: 1-16.
• Ma WC, Minda D, 1992. A unified treatment of some special classes of univalent functions. Proc. Conf. On Complex Analysis, 157-169.
• Miller SS, Mocanu PT, 2000. Differential Subordinations: Theory and Applications, Marcel Dekker, New York, USA.
• Seoudy TM, Aouf MK, 2016. Coefficient estimates of new classes of q-starlike and q-convex functions of complex order. J. Math. Inequal. 10(1): 135-145.
• Srivastava HM, Raza N, Abujarad ESA, Srivastava G, Abujarad MH, 2019. Fekete-Szegö inequality for classes of (p,q)-Starlike and (p,q)-Convex functions. RASCAM (113): 3563-3584.
• Uçar HEÖ, 2016. Coefficient inequality for q-starlike functions. Appl. Math. Comput. (276): 122-126.