The main object of this paper is to investigate the convolution of a subclass of harmonic univalent mappings which is denoted by fa and generalized harmonic univalent mapping which is denoted by Pc. We obtained Pc ∗ fa is univalent and convex in the horizantal direction for 0 < c ≤ 2 1−a 1+a . In addition, we present an example and illustrate it graphically with the help of Maple to explain the behaviour of image domain
Clunie, J., Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I. Math., 9, pp. 3-25.
Duren, P., (2004), Harmonic mappings in the Plane, Cambridge Tracts in Mathematics 156, Cam- bridge Univ. Press, Cambridge.
Dorff, M., Suffridge, T., (1997), The inner mapping radius of harmonic mappings of the unit disk, Complex Var. Theory Appl., 33, pp. 97-103.
Dorff, M., (2001), Convolutions of planar harmonic convex mappings, Complex Var. Theorey Appl., 45, pp. 263-271.
Dorff, M., Nowak, M., Woloszkiewicz, M., (2012), Convolutions of harmonic convex mappings, Com- plex Var. Elliptic Equ., 57(5), pp. 486-503.
Liu, Z., Li, Y., (2013), The properties of a new subclass of harmonic univalent mappings, Abstr. Appl. Anal. Article ID 794108.
Wang, Z., Liu, Z., Li, Y., (2016), On convolutions of harmonic univalent mappings convex in the direction of the real axis, J. Appl. Anal. Comput., 6(1), pp. 145-155.
Boyd, Z., Dorff, M., Nowak, M., Romney, M., Woloszkiewicz, M., (2014), Univalency of convolutions of harmonic mappings, Appl. Math. Comp., 234, pp. 326-332.
Li, Y., Liu, Z., (2016), Convolutions of harmonic right half plane mappings, Open Math., 14, pp.789- 800.
Rahman, Q. T., Schmeisser, G., (2002), Analytic theory of polynomials, London Mathematical Society Monigraphs New Series 26, Oxford Univ. Press, Oxford.
Year 2020,
Volume: 10 Issue: 2, 353 - 359, 01.03.2020
Clunie, J., Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I. Math., 9, pp. 3-25.
Duren, P., (2004), Harmonic mappings in the Plane, Cambridge Tracts in Mathematics 156, Cam- bridge Univ. Press, Cambridge.
Dorff, M., Suffridge, T., (1997), The inner mapping radius of harmonic mappings of the unit disk, Complex Var. Theory Appl., 33, pp. 97-103.
Dorff, M., (2001), Convolutions of planar harmonic convex mappings, Complex Var. Theorey Appl., 45, pp. 263-271.
Dorff, M., Nowak, M., Woloszkiewicz, M., (2012), Convolutions of harmonic convex mappings, Com- plex Var. Elliptic Equ., 57(5), pp. 486-503.
Liu, Z., Li, Y., (2013), The properties of a new subclass of harmonic univalent mappings, Abstr. Appl. Anal. Article ID 794108.
Wang, Z., Liu, Z., Li, Y., (2016), On convolutions of harmonic univalent mappings convex in the direction of the real axis, J. Appl. Anal. Comput., 6(1), pp. 145-155.
Boyd, Z., Dorff, M., Nowak, M., Romney, M., Woloszkiewicz, M., (2014), Univalency of convolutions of harmonic mappings, Appl. Math. Comp., 234, pp. 326-332.
Li, Y., Liu, Z., (2016), Convolutions of harmonic right half plane mappings, Open Math., 14, pp.789- 800.
Rahman, Q. T., Schmeisser, G., (2002), Analytic theory of polynomials, London Mathematical Society Monigraphs New Series 26, Oxford Univ. Press, Oxford.