scholarly journals Some differential inequalities in the complex plane

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 29-34
Author(s):  
Mamoru Nunokawa ◽  
Oh Kwon ◽  
Young Sim ◽  
Ji Park ◽  
Nak Cho
Keyword(s):  
Complex Plane ◽  
Convex Functions ◽  
Second Order ◽  
Differential Inequalities ◽  
Differential Subordinations

In the present paper, we obtain some new results by applying well-known Jack?s lemma. Moreover, the second-order differential subordinations associated with convex functions are also considered.

scholarly journals Study on new integral operators defined using confluent hypergeometric function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Georgia Irina Oros
Keyword(s):  
Hypergeometric Function ◽  
Complex Plane ◽  
Convex Functions ◽  
Univalent Functions ◽  
Integral Operators ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Starlike And Convex Functions ◽  
Inclusion Properties ◽  
Admissible Functions

AbstractTwo new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order $\frac{1}{2}$ 1 2 and convexity of order $\frac{1}{2}$ 1 2 to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals Focal Subfunctions and Second Order Differential Inequalities

1991 ◽  
Vol 21 (3) ◽  
pp. 1127-1141 ◽  
Author(s):  
S. Umamaheswaram ◽  
M. Venkata Rama
Keyword(s):  
Second Order ◽  
Differential Inequalities

8.—On Second-order Differential Inequalities

1974 ◽  
Vol 72 (2) ◽  
pp. 109-127 ◽  
Author(s):  
F. V. Atkinson
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Second Order ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisThis paper is devoted to a study of differential equations and inequalities of the formandThe results are mainly concerned with the existence of positive solutions, their uniqueness in the case of (*), and bounds for these solutions.

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