A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions

ABSTRACT

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

KEYWORDS

Harmonic Univalent Starlike Functions, Harmonic Convex Functions, Wright Hypergeometric Functions, Raina-Dziok Operator, Distortion Bounds, Extreme Points

Harmonic Univalent Starlike Functions, Harmonic Convex Functions, Wright Hypergeometric Functions, Raina-Dziok Operator, Distortion Bounds, Extreme Points

Cite this paper

nullG. Murugusundaramoorthy and K. Vijaya, "A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions,"*Applied Mathematics*, Vol. 1 No. 2, 2010, pp. 87-93. doi: 10.4236/am.2010.12011.

nullG. Murugusundaramoorthy and K. Vijaya, "A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions,"

References

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[2] E. M. Wright, “The Asymptotic Expansion of the Generalized Hypergeometric Function,” Proceedings of the London Mathematical Society, Vol. 46, 1946, pp. 389-408.

[3] J. Dziok and H. M. Srivastava, “Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function,” Integral Transforms and Special Functions, Vol. 14, No. 1, 2003, pp. 7-18.

[4] J. Dziok and R. K. Raina, “Families of Analytic Functions Associated with the Wright Generalized Hypergeometric Function,” Demonstratio Mathematica, Vol. 37, No. 3, 2004, pp. 533-542.

[5] J. M. Jahangiri, “Harmonic Functions Starlike in the Unit Disc,” Journal of Mathematical Analysis and Applications, Vol. 235, No. 2, 1999, pp. 470-477.

[6] B. C. Carlson and D. B. Sha?er, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 737-745.

[7] S. Ruscheweyh, “New Criteria for Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 49, No. 1, 1975, pp. 109-115.

[8] H. M. Srivastava and S. Owa, “Some Characterization and Distortion Theorems Involving Fractional Calculus, Generalized Hypergeometric Functions, Hadamard Products, Linear Operators and Certain Subclasses of Analytic Functions,” Nagoya Mathematics Journal, Vol. 106, 1987, pp. 1-28.

[9] Y. Avici and E. Zlotkiewicz, “On Harmonic Univalent Mappings,” Annales Universitatis Mariae Curie-Sk?odowska, Sectio A, Vol. 44, 1990, pp. 1-7.

[10] J. M. Jahangiri and H. Silverman, “Harmonic Univalent Functions with Varying Arguments,” International Journal of Applied Mathematics, Vol. 8, No. 3, 2002, pp. 267- 275.

[11] J. M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, “Starlikeness of Rucheweyh Type Harmonic Univalent Functions,” Journal of the Indian Academy of Mathematics, Vol. 26, No. 1, 2004, pp. 191-200.

[12] G. Murugusundaramoorthy, “A Class of Ruscheweyh-Type Harmonic Univalent Functions with Varying Arguments,” Southwest Journal of Pure and Applied Mathematics, No. 2, 2003, pp. 90-95.

[13] K. Vijaya, “Studies on Certain Subclasses of Harmonic Functions,” Ph.D. Thesis, Vellore Institute of Technology University, Vellore, September 2006.

[14] S. Ruscheweyh, “Neighborhoods of Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 81, No. 4, 1981, pp. 521-528.

[1] J. Clunie and T. Sheil-Small, “Harmonic Univalent Functions,” Annales Academiae Scientiarum Fennicae, Series A I, Mathematica, Vol. 9, 1984, pp. 3-25.

[2] E. M. Wright, “The Asymptotic Expansion of the Generalized Hypergeometric Function,” Proceedings of the London Mathematical Society, Vol. 46, 1946, pp. 389-408.

[3] J. Dziok and H. M. Srivastava, “Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function,” Integral Transforms and Special Functions, Vol. 14, No. 1, 2003, pp. 7-18.

[4] J. Dziok and R. K. Raina, “Families of Analytic Functions Associated with the Wright Generalized Hypergeometric Function,” Demonstratio Mathematica, Vol. 37, No. 3, 2004, pp. 533-542.

[5] J. M. Jahangiri, “Harmonic Functions Starlike in the Unit Disc,” Journal of Mathematical Analysis and Applications, Vol. 235, No. 2, 1999, pp. 470-477.

[6] B. C. Carlson and D. B. Sha?er, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 737-745.

[7] S. Ruscheweyh, “New Criteria for Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 49, No. 1, 1975, pp. 109-115.

[8] H. M. Srivastava and S. Owa, “Some Characterization and Distortion Theorems Involving Fractional Calculus, Generalized Hypergeometric Functions, Hadamard Products, Linear Operators and Certain Subclasses of Analytic Functions,” Nagoya Mathematics Journal, Vol. 106, 1987, pp. 1-28.

[9] Y. Avici and E. Zlotkiewicz, “On Harmonic Univalent Mappings,” Annales Universitatis Mariae Curie-Sk?odowska, Sectio A, Vol. 44, 1990, pp. 1-7.

[10] J. M. Jahangiri and H. Silverman, “Harmonic Univalent Functions with Varying Arguments,” International Journal of Applied Mathematics, Vol. 8, No. 3, 2002, pp. 267- 275.

[11] J. M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, “Starlikeness of Rucheweyh Type Harmonic Univalent Functions,” Journal of the Indian Academy of Mathematics, Vol. 26, No. 1, 2004, pp. 191-200.

[12] G. Murugusundaramoorthy, “A Class of Ruscheweyh-Type Harmonic Univalent Functions with Varying Arguments,” Southwest Journal of Pure and Applied Mathematics, No. 2, 2003, pp. 90-95.

[13] K. Vijaya, “Studies on Certain Subclasses of Harmonic Functions,” Ph.D. Thesis, Vellore Institute of Technology University, Vellore, September 2006.

[14] S. Ruscheweyh, “Neighborhoods of Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 81, No. 4, 1981, pp. 521-528.