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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제36권 제5호
- 발행연도
- 2018.1
- 수록면
- 567 - 574 (8page)
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Let $f:f(z)=z+{\sum^{{\infty}}_{n=2}}a_nz^n$ be analytic in the open unit disc E. Then f is said to belong to the class $M_{\alpha}$ of alpha-convex functions, if it satisfies the condition ${\Re}\{(1-{{\alpha})}{\frac{zf^{\prime}(z)}{f(z)}}+{{\alpha}}{\frac{(zf^{\prime}(z))^{\prime})}{f^{\prime}(z)}}\}$ > 0, ($z{\in}E$). In this paper, we introduce and study q-analogue of the class $M_{\alpha}$ by using concepts of Quantum Analysis. It is shown that the functions in this new class $M(q,{\alpha})$ are q-starlike. A problem related to q-Bernardi operator is also investigated.
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참고문헌 (13)
참고문헌 신청
K. Ademogullari / 2016 / q-harmonic mappings for which analytic part is q-convex function / Nonlinear Anal. Diff. Eqns 4:283~293
M. H. Ismail / 1990 / A generalization of starlike functions / Complex Var. Elliptic Eqns 14:77~84
F. H. Jackson / 1909 / On q-functions and certain difference operators / Trans. Roy. Soc. Edinburgh 46:253~281
F. H. Jackson / 1910 / On q-definite integrals / Q. J. Math 41:193~203
S. S. Miller / 1973 / All α-convex functions are starlike / Proc. Amer. Math. Soc 37:553~554
M. H. Ismail / 1990 / A generalization of starlike functions / Complex Var. Elliptic Eqns 14:77~84
F. H. Jackson / 1909 / On q-functions and certain difference operators / Trans. Roy. Soc. Edinburgh 46:253~281
F. H. Jackson / 1910 / On q-definite integrals / Q. J. Math 41:193~203
S. S. Miller / 1973 / All α-convex functions are starlike / Proc. Amer. Math. Soc 37:553~554
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