Convolution Conditions for (p,q)-Convexity, (p,q)-Starlikeness and (p,q)-Spirallikeness
Résumé
In the present investigation, we derive the necessary and sufficient conditions for $(p,q)$-starlike, $(p,q)$-convex functions of order $\mu$ and $(p,q)$-spirallike, convex $(p,q)$-spirallike functions using convolution.
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Références
\bibitem{mama} Chakrabarti, R. and Jagannathan, R., {\it A {{\((p,q)\)}}-oscillator realization of two-parameter quantum algebras}, J. Phys. A, Math. Gen.,
24(13), l711--l718, (1991).
\bibitem{Talal4} Hamid, S. and Latha, S., {\it Convolution conditions for $q$-Convexity, $q$-Starlikeness and $q$-Spirallikeness}, TWMS J. Appl. Eng. Math., 12(3),
1032--1038, (2022).
\bibitem{hamid1} P{\'o}lya, G. and Schoenberg, I. J., {\it Remarks on de la {Vall{\'e}e} {Poussin} means and convex conformal maps of the circle}, Pac. J. Math., 8, 295--334, (1958).
\bibitem{hamid4} Ruscheweyh, S. and Sheil-Small, T., {\it Hadamard products of schlicht functions and the {Polya}-{Schoenberg} conjecture}, Comment. Math. Helv.,
48, 119--135, (1973).
\bibitem{hamid3} Ruscheweyh, S., {\it Linear operators between classes of prestarlike functions}, Comment. Math. Helv., 52, 497--509, (1977).
\bibitem{hamid2} Silverman, H., Silvia, E. M. and Telage, D., {\it Convolution conditions for convexity starlikeness, and spiral-likeness},
Math. Z., 162, 125--130, (1978).
\bibitem{hamid6} Suffridge, T. J., {\it Starlike functions as limits of polynomials}, {Lect}. {Notes} {Math}. 505, 164--203, (1976).
24(13), l711--l718, (1991).
\bibitem{Talal4} Hamid, S. and Latha, S., {\it Convolution conditions for $q$-Convexity, $q$-Starlikeness and $q$-Spirallikeness}, TWMS J. Appl. Eng. Math., 12(3),
1032--1038, (2022).
\bibitem{hamid1} P{\'o}lya, G. and Schoenberg, I. J., {\it Remarks on de la {Vall{\'e}e} {Poussin} means and convex conformal maps of the circle}, Pac. J. Math., 8, 295--334, (1958).
\bibitem{hamid4} Ruscheweyh, S. and Sheil-Small, T., {\it Hadamard products of schlicht functions and the {Polya}-{Schoenberg} conjecture}, Comment. Math. Helv.,
48, 119--135, (1973).
\bibitem{hamid3} Ruscheweyh, S., {\it Linear operators between classes of prestarlike functions}, Comment. Math. Helv., 52, 497--509, (1977).
\bibitem{hamid2} Silverman, H., Silvia, E. M. and Telage, D., {\it Convolution conditions for convexity starlikeness, and spiral-likeness},
Math. Z., 162, 125--130, (1978).
\bibitem{hamid6} Suffridge, T. J., {\it Starlike functions as limits of polynomials}, {Lect}. {Notes} {Math}. 505, 164--203, (1976).
Publiée
2026-03-23
Rubrique
Research Articles
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