In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon....In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.展开更多
We studied the monotonicity and Convexity properties of the new functions involving the gamma function, and get the general conclusion that Minc-Sathre and C. P. Chen-G. Wang’s inequality are extended and refined.
Let S<sup>*</sup> be the class of starlike functions in unit disc.For f∈S<sup>*</sup>,denote its radiusof convexity by r<sub>0</sub> and let d<sub>0</sub>=（?）|f（z）|...Let S<sup>*</sup> be the class of starlike functions in unit disc.For f∈S<sup>*</sup>,denote its radiusof convexity by r<sub>0</sub> and let d<sub>0</sub>=（?）|f（z）|,d<sup>*</sup>=inf{|β||f（z）≠β,|z|【1}.In this paper weprove d<sub>0</sub>/d<sup>*</sup>≥0.45,thus improving the result of d<sub>0</sub>/d<sup>*</sup>≥0.38 by McCarty,C.P.and Tepper,D.E.and d<sub>0</sub>/d<sup>*</sup>≥0.41 by Huang Xinzhong.展开更多
In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s ...In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.展开更多
The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Fr...The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.展开更多
Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programmin...Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.展开更多
文摘In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.
文摘We studied the monotonicity and Convexity properties of the new functions involving the gamma function, and get the general conclusion that Minc-Sathre and C. P. Chen-G. Wang’s inequality are extended and refined.
文摘Let S<sup>*</sup> be the class of starlike functions in unit disc.For f∈S<sup>*</sup>,denote its radiusof convexity by r<sub>0</sub> and let d<sub>0</sub>=（?）|f（z）|,d<sup>*</sup>=inf{|β||f（z）≠β,|z|【1}.In this paper weprove d<sub>0</sub>/d<sup>*</sup>≥0.45,thus improving the result of d<sub>0</sub>/d<sup>*</sup>≥0.38 by McCarty,C.P.and Tepper,D.E.and d<sub>0</sub>/d<sup>*</sup>≥0.41 by Huang Xinzhong.
文摘In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be compared to that of Simpson’s formula in Applied Math. Lett. (24) (2011), 1565-1568.
文摘The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.
文摘Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.
