scholarly journals On the Jack lemma and its generalization

2020 ◽  
Vol 107 (121) ◽  
pp. 63-65
Author(s):  
Mamoru Nunokawa ◽  
Nak Cho ◽  
Janusz Sokół
Keyword(s):  
Geometric Approach ◽  
Differential Subordination ◽  
Subordination Theory

We present a new geometric approach to some problems in differential subordination theory and discuss the new results closely related to the Jack lemma.

Some applications of first-order differential subordinations

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Differential Subordination ◽  
First Order ◽  
Carathéodory Functions ◽  
Subordination Theory ◽  
Differential Subordinations

AbstractIn this work we present a new geometric approach to some problems in differential subordination theory. In the paper some sufficient conditions for function to be starlike or univalent or to be in the class of Carathéodory functions are obtained. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

scholarly journals Differential subordination for Janowski functions with positive real part

2021 ◽  
Vol 66 (3) ◽  
pp. 457-470
Author(s):  
Swati Anand ◽  
V. Ravichandran ◽  
Sushil Kumar
Keyword(s):  
Sufficient Conditions ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Positive Real Part ◽  
Algebraic Condition ◽  
Positive Real ◽  
First Order ◽  
Janowski Functions ◽  
Subordination Theory ◽  
Differential Subordinations

"Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition.We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Janowski function with positive real part. As applications, we obtain suffcient conditions for normalized analytic functions to be Janowski starlike functions."

scholarly journals Subclasses of Multivalent Analytic Functions Associated with a q-Difference Operator

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2184
Author(s):  
Ekram Elsayed Ali ◽  
Teodor Bulboacă
Keyword(s):  
Analytic Functions ◽  
Difference Operator ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Inclusion Properties ◽  
Subordination Theory

In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the q-derivative operator. With the aid of the Jackson q-derivative we defined two new operators that generalize many other previously studied operators, and help us to define two new subclasses of functions with several interesting properties studied in this paper. The methods used for the proof of our results are special tools of the differential subordination theory of one-variable functions.

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory

A GEOMETRIC APPROACH TO DISSIPATION AND ITS APPLICATION TO DISSIPATIVE NUCLEAR DYNAMICS

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-87-C6-94
Author(s):  
H. Reinhardt ◽  
R. Balian ◽  
Y. Alhassid
Keyword(s):  
Geometric Approach ◽  
Nuclear Dynamics

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

scholarly journals On Certain Differential Subordination of Harmonic Mean Related to a Linear Function

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 966
Author(s):  
Anna Dobosz ◽  
Piotr Jastrzębski ◽  
Adam Lecko
Keyword(s):  
Convex Function ◽  
Linear Function ◽  
Differential Subordination ◽  
Harmonic Mean ◽  
Best Dominant ◽  
Symmetry Properties ◽  
Differential Subordinations ◽  
Difficult Issue

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

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