scholarly journals Univalence criteria for a nonlinear integral operator

2011 ◽  
Vol 42 (1) ◽  
Author(s):  
C. Selvaraj ◽  
K.A. Selvakumaran
Keyword(s):  
Integral Operator ◽  
Nonlinear Integral Operator ◽  
Univalence Criteria

scholarly journals Univalence criteria for a nonlinear integral operator

2011 ◽  
Vol 42 (1) ◽  
pp. 79-85
Author(s):  
C. Selvaraj ◽  
K. A. Selvakumaran
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Integral Transform ◽  
Geometric Properties ◽  
Nonlinear Integral Operator ◽  
Univalence Criteria

The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.

Univalence criteria for a general integral operator

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 11-19 ◽  
Author(s):  
Erhan Deniz
Keyword(s):  
Integral Operator ◽  
General Integral ◽  
Significant Relationships ◽  
General Integral Operator ◽  
Univalence Criteria

In this paper the author introduces a general integral operator and determines conditions for the univalence of this integral operator. Also, the significant relationships and relevance with other results are also given.

scholarly journals Bifurcation of Bounded Solutions of Impulsive Differential Equations

2016 ◽  
Vol 26 (14) ◽  
pp. 1650242 ◽  
Author(s):  
Kevin E. M. Church ◽  
Xinzhi Liu
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Necessary Condition ◽  
Bounded Solutions ◽  
Pitchfork Bifurcations ◽  
Nonlinear Integral Operator

In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results.

scholarly journals A Connection between Basic Univalence Criteria

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Horiana Tudor
Keyword(s):  
Integral Operator ◽  
Sufficient Condition ◽  
Univalence Criteria ◽  
Class Of Functions

We obtain a sufficient condition for the analyticity and the univalence of a class of functions defined by an integral operator. The well-known univalence criteria of Alexander, Noshiro-Warschawski, Nehari, Goluzin, Ozaki-Nunokawa, Becker, and Lewandowski would follow upon specializing the functions and the parameters involved in the main result. The results obtained not only reduce to those earlier works, but they also extend the previous results.

scholarly journals On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Baghani ◽  
O. Baghani
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Operator

The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.

scholarly journals Blow-up and global existence for a kinetic equation of swarm formation

2017 ◽  
Vol 27 (06) ◽  
pp. 1153-1175 ◽  
Author(s):  
Mirosław Lachowicz ◽  
Henryk Leszczyński ◽  
Martin Parisot
Keyword(s):  
Asymptotic Behavior ◽  
Kinetic Equation ◽  
Global Existence ◽  
Integral Operator ◽  
Blow Up ◽  
Existence Of Solutions ◽  
Interaction Rate ◽  
Global Existence Of Solutions ◽  
Nonlinear Integral Operator ◽  
The Right

In this paper we study a kinetic equation that describes swarm formations. The right-hand side of this equation contains nonlinear integro-differential terms responsible for two opposite tendencies: dissipation and swarming. The nonlinear integral operator describes the changes of velocities (orientations) of interacting individuals. The interaction rate is assumed to be dependent of velocities of interacting individuals. Although the equation seems to be rather simple it leads to very complicated dynamics. In this paper, we study possible blow-ups versus global existence of solutions and provide results on the asymptotic behavior. The complicated dynamics and possibility of blow-ups can be directly related to creation of swarms.

scholarly journals Some univalence conditions related to a general integral operator

2020 ◽  
Vol 28 (2) ◽  
pp. 33-47
Author(s):  
Camelia Bărbatu ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Recent Work ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral ◽  
General Integral Operator ◽  
Univalence Criteria

AbstractFor some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢n, that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.

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