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ON A CLASS OF QUANTUM ALPHA-CONVEX FUNCTIONS
KHALIDA INAYAT NOOR,RIZWAN S. BADAR 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
Let f : f(z) = z + Σ∞ n=2 anzn be analytic in the open unit disc E: Then f is said to belong to the class M of alpha-convex functions, if it satisfies the condition ℜ { (1 − ) zf′(z) f(z) + (zf′(z))′ f′(z) } > 0; (z ∈ E): In this paper, we introduce and study q-analogue of the class M by using concepts of Quantum Analysis. It is shown that the functions in this new class M(q; ) are q-starlike. A problem related to q-Bernardi operator is also investigated.
ON A CLASS OF QUANTUM ALPHA-CONVEX FUNCTIONS
NOOR, KHALIDA INAYAT,BADAR, RIZWAN S. The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5
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.