Abstract
This paper aims to introduce the q-analogue of subclasses of the spiral-like functions of complex order and derive some inclusion properties by applying certain linear operators. The invariance of these classes under q-Bernardi integral operator has been discussed. Our results yield some known results as special case.
(Communicated by Stanisława Kanas)
References
[1] Adams, C. R.: On the linear ordinary q-difference equation Ann. Math. 30 (1929), 195–205.10.2307/1968274Suche in Google Scholar
[2] Agarwal, S.Sahoo, S. K.: A generalization of starlike functions of order alpha Hokkaido Math. J. 46 (2017), 15–27.10.14492/hokmj/1498788094Suche in Google Scholar
[3] Altintas, O.Mustafa, N.: Coefficient bounds and distortion theorems for the certain analytic functions Turkish J. Math. 43 (2019), 985–997.10.3906/mat-1812-85Suche in Google Scholar
[4] Arif, M.Ul-Haq, M.Liu, J. L.: A subfamily of univalent functions associated with q-analogue of Noor integral operator J. Funct Spaces 2018 (2018), Art. ID 3818915.10.1155/2018/3818915Suche in Google Scholar
[5] Carmichael, R. D.: The general theory of linear q-difference equations Amer. J. Math. 34 (1912), 147–168.10.2307/2369887Suche in Google Scholar
[6] Choi, J. H.: Applications for certain classes of spirallike functions defined by the Srivastava-Attiya operator Adv. Pure Math. 8 (2018), 615–623.10.4236/apm.2018.86035Suche in Google Scholar
[7] Exton, H.: q-Hypergeometric Functions and Applications Ellis Horwood Limited, Chichester, UK, 1983.Suche in Google Scholar
[8] Gasper, G.Rahman, M.: Basic Hypergeometric Series Cambridge University Press, Cambridge, UK, 1990.Suche in Google Scholar
[9] Ghany, H. A.: q-derivative of basic hypergeomtric series with respect to parameters Int. J. Math. Anal. 3 (2009), 1617–1632.Suche in Google Scholar
[10] Govindaraj, M.Sivasubramanian, S.: On a class of analytic functions related to conic domains involving q-calculus Anal. Math. 43 (2017), 475–487.10.1007/s10476-017-0206-5Suche in Google Scholar
[11] Ismail, M. E. H.Merkes, E.Styer, D.: A generalization of starlike functions Comp. Var. Theory Appl. 14 (1990), 77–84.10.1080/17476939008814407Suche in Google Scholar
[12] Jackson, F. H.: On q-definite integrals Quart. J. Pure Appl. Math. 41 (1910), 193–203.Suche in Google Scholar
[13] Jackson, F. H.: On q-functions and a certain difference operator Trans. Roy. Soc. Edin. 46 (1908), 253–281.10.1017/S0080456800002751Suche in Google Scholar
[14] Kanas, S.Raducanu, D.: Some classes of analytic functions related to Conic domains Math. Slovaca 64 (2014), 1183–1196.10.2478/s12175-014-0268-9Suche in Google Scholar
[15] Koc, V.Cheung, P.: Quantum Calculus Springer, Berlin, Germany, 2001.Suche in Google Scholar
[16] Noor, K. I.: On generalized q-close-to-convexity Appl. Math. Inf. Sci. 11 (2017), 1383–1388.10.18576/amis/110515Suche in Google Scholar
[17] Noor, K. I.Bukhari, S. Z. H.: Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava-Attiya integral operator Integral Transforms Spec. Funct. 21 (2010), 907–916.10.1080/10652469.2010.487305Suche in Google Scholar
[18] Noor, K. I.Riaz, S.: Generalized q-starlike functions Studia Sci. Math. Hungar. 54 (2017), 509–522.10.1556/012.2017.54.4.1380Suche in Google Scholar
[19] Noor, K. I.Riaz, S.Noor, M. A.: On q-Bernardi integral operator TWMS J. Pure Appl. Math. 8 (2017), 3–11.10.18576/amis/110523Suche in Google Scholar
[20] Raghavendar, K.Swaminathan, A.: Close-to-convexity of basic hypergeometric functions using their Taylor coefficients J. Math. Appl. 35 (2012), 111–125.10.7862/rf.2012.5Suche in Google Scholar
[21] Shah, S. A.Noor, K. I.: Study on q-analogue of certain family of linear operators Turkish J. Math. 43 (2019), 2707–2714.10.3906/mat-1907-41Suche in Google Scholar
[22] Shamsan, H. Latha, S.: On genralized bounded Mocanu variation related to q-derivative and conic regions Annals Pure Appl. math. 17 (2018), 67–83.10.22457/apam.v17n1a8Suche in Google Scholar
[23] Srivastava, H. M. Attiya, A. A.: An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination Integral Transforms Spec. Funct. 8 (2007), 207–216.10.1080/10652460701208577Suche in Google Scholar
[24] Srivastava, H. M.Choi, J.: Series Associated with Zeta and Related Function Kluwer Academic Publisher, Dordrecht, 2001.10.1007/978-94-015-9672-5Suche in Google Scholar
[25] 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.Suche in Google Scholar
[26] Trijitzinsky, W. J.: Analytic theory of linear q-difference equations Acta Math. 61 (1933), 1–38.10.1007/BF02547785Suche in Google Scholar
[27] Ucar, H. E. Ö.: Coefficient inequality for q-starlike functions Appl. Math. Comput. 276 (2016), 122–126.10.1016/j.amc.2015.12.008Suche in Google Scholar
[28] Ucar, H. E. Ö.Mert, O.Polatoglu, Y.: Some properties of q-close-to-convex functions Hacet. J. Math. Stat. 46 (2017), 1105–1112.10.15672/HJMS.2017.459Suche in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
- Doc. RNDr. Roman Frič, DrSc. passed away
- Outer and inner approximations in quantum spaces
- Linear derivations on Banach *-algebras
- New fractional order discrete Grüss type inequality
- Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
- Generalized Minkowski type inequality for pseudo-integral
- Study of the Q-spiral-like functions of complex order
- Radius of starlikeness of certain analytic functions
- Successive approximations for a differential equation in a Banach space via Constantin condition
- Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
- Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
- Sequence selection properties in Cp(X) with the double ideals
- On the paranormed Nörlund difference sequence space of fractional order and geometric properties
- On certain Diophantine equations concerning the area of right triangles
- Weighted projective Ricci curvature in Finsler geometry
- Euler classes of vector bundles over manifolds
- A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
- Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
- The (α, β)-ramification invariants of a number field
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
- Doc. RNDr. Roman Frič, DrSc. passed away
- Outer and inner approximations in quantum spaces
- Linear derivations on Banach *-algebras
- New fractional order discrete Grüss type inequality
- Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
- Generalized Minkowski type inequality for pseudo-integral
- Study of the Q-spiral-like functions of complex order
- Radius of starlikeness of certain analytic functions
- Successive approximations for a differential equation in a Banach space via Constantin condition
- Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
- Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
- Sequence selection properties in Cp(X) with the double ideals
- On the paranormed Nörlund difference sequence space of fractional order and geometric properties
- On certain Diophantine equations concerning the area of right triangles
- Weighted projective Ricci curvature in Finsler geometry
- Euler classes of vector bundles over manifolds
- A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
- Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
- The (α, β)-ramification invariants of a number field