Research ArticleOpen AccessGoogle Scholar indexed
Applications for Certain Classes of Spirallike Functions Defined by the Srivastava-Attiya Operator
Department of Mathematics Education, Daegu National University of Education, Daegu, Korea
- 1 Department of Mathematics Education, Daegu National University of Education, Daegu, Korea
Advances in Pure Mathematics·Volume 08 (2018)·Pages 615–623·Published 20 June 2018·DOI10.4236/apm.2018.86035
Copy link · social · email
Abstract
Let the function f be analytic in U={z:z ∈C and < 1} and be given by . In this paper, making use of the Srivastava-Attiya operator L s,b , we introduce two classes of analytic functions and investigate some convolution properties and coefficient estimates for these classes. Furthermore, several inclusion properties involving these and other families of integral operators are also considered.
KeywordsAnalytic FunctionHadamard ProductSubordinationSrivastava-Attiya Operator
- Bhoosnurmath, S.S. and Devadas, M.V. (1996) Subclasses of Spirallike Functions Defined by Subordination. Journal of Analysis Madras, 4, 173-183.
- Bhoosnurmath, S.S. and Devadas, M.V. (1997) Subclasses of Spirallike Functions Defined by Ruschweyh Derivatives. Tamkang Journal of Mathematics, 28, 59-65.
- Nikitin, S.V. (1987) A Class of Regular Functions, Current Problem in Function Theory (in Russian). Teberda 1985, Rostov Gos. Univ., Rostov-on-Don, 143-147.
- Ahuja, O.P. (1993) Families of Analytic Functions Related to Ruscheweyh Derivatives and Subordinate to Convex Functions. Yokohama Mathematical Journal, 41, 39-50.
- Goel, R.M. and Mehrok, B.S. (1981) On the Coefficients of a Subclass of Starlike Functions. Indian Journal of Pure and Applied Mathematics, 12, 634-647.
- Silverman, H. and Silvia, E.M. (1985) Subclasses of Starlike Functions Subordinate to Convex Functions. Canadian Journal of Mathematics, 1, 48-61. https://doi.org/10.4153/CJM-1985-004-7
- Spacek, L. (1932) Contribution à la theorie des fonctions univalents. Casopis pro Pestovani Matematiky Fysiky, 62, 12-19.
- Srivastava, H.M. and Choi, J. (2001) Series Associated with the Zeta and Related Function. Kluwer Academic Publishers, Dordrecht. https://doi.org/10.1007/978-94-015-9672-5
- Ferreira, C. and Lopez, J.L. (2004) Asymptotic Expansions of the Hurwitz-Lerch Zeta Function. Journal of Mathematical Analysis and Applications, 298, 210-224. https://doi.org/10.1016/j.jmaa.2004.05.040
- Lin, S.D., Srivastava, H.M. and Wang, P.Y. (2006) Some Expansion Formulas for a Class of Generalized Hurwitz-Lerch Zeta Functions. Integral Transforms and Special Functions, 17, 817-827. https://doi.org/10.1080/10652460600926923
- Srivastava, H.M., Jankov, D., Pogány, T.K. and Saxena, R.K. (2011) Two-Side Inequalities for the Extended Hurwitz-Lerch Zeta Function. Computers & Mathematics with Applications, 62, 516-522.
- Srivastava, H.M. and Attiya, A.A. (2007) An Integral Operator Associated with the Hurwitz-Lerch Zeta Function and Differential Subordination. Integral Transforms and Special Functions, 18, 207-216. https://doi.org/10.1080/10652460701208577
- Liu, J.L. (2011) Sufficient Conditions for Strongly Starlike Functions Involving the Generalized Srivastava-Attiya Operator. Integral Transforms and Special Functions, 22, 79-90. https://doi.org/10.1080/10652469.2010.498110