scholarly journals Some Janowski Type Harmonic q-Starlike Functions Associated with Symmetrical Points

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 629 ◽  
Author(s):  
Muhammad Arif ◽  
Omar Barkub ◽  
Hari Srivastava ◽  
Saleem Abdullah ◽  
Sher Khan
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Partial Sums ◽  
Circular Region ◽  
Necessary And Sufficient ◽  
New Criterion ◽  
Symmetrical Points ◽  
Convexity Conditions

The motive behind this article is to apply the notions of q-derivative by introducing some new families of harmonic functions associated with the symmetric circular region. We develop a new criterion for sense preserving and hence the univalency in terms of q-differential operator. The necessary and sufficient conditions are established for univalency for this newly defined class. We also discuss some other interesting properties such as distortion limits, convolution preserving, and convexity conditions. Further, by using sufficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic functions to its sequences of partial sums. Some known consequences of the main results are also obtained by varying the parameters.

scholarly journals A Subclass of Janowski Starlike Functions Involving Mathieu-Type Series

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 2
Author(s):  
Dong Liu ◽  
Serkan Araci ◽  
Bilal Khan
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Function Class ◽  
Partial Sums ◽  
Invariant Functions ◽  
Type Series ◽  
Janowski Functions ◽  
Radius Problems ◽  
Symmetrical Points

To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

scholarly journals On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1947
Author(s):  
Saira Zainab ◽  
Mohsan Raza ◽  
Qin Xin ◽  
Mehwish Jabeen ◽  
Sarfraz Nawaz Malik ◽  
...  
Keyword(s):  
Differential Operator ◽  
Starlike Functions ◽  
Partial Sums ◽  
Open Unit ◽  
New Class ◽  
Conic Domain ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Coefficient Bound ◽  
Necessary And Sufficient

Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class k−STqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class k−STqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included.

Necessary and sufficient conditions for asymptotic decay of oscillations in delayed functional equations

1981 ◽  
Vol 91 (1-2) ◽  
pp. 135-145
Author(s):  
Lu-San Chen ◽  
Cheh-Chih Yeh
Keyword(s):  
Differential Operator ◽  
Functional Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Oscillatory Solutions ◽  
Asymptotic Decay ◽  
Image Position ◽  
Necessary And Sufficient

SynopsisThis paper studies the equationwhere the differential operator Ln is defined byand a necessary and sufficient condition that all oscillatory solutions of the above equation converge to zero asymptotically is presented. The results obtained extend and improve previous ones of Kusano and Onose, and Singh, even in the usual case wherewhere N is an integer with l≦N≦n–1.

On Janowski harmonic functions

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
Necessary And Sufficient

AbstractIn this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.

scholarly journals A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares

2008 ◽  
Vol 40 (04) ◽  
pp. 1198-1222
Author(s):  
Donatas Surgailis
Keyword(s):  
Stationary Solution ◽  
Long Memory ◽  
Sufficient Conditions ◽  
Partial Sums ◽  
Finite Variance ◽  
Fourth Moment ◽  
Stable Limit ◽  
Arch Model ◽  
Necessary And Sufficient ◽  
Special Case

We introduce a modification of the linear ARCH (LARCH) model (Giraitis, Robinson, and Surgailis (2000)) - a special case of Sentana's (1995) quadratic ARCH (QARCH) model - for which the conditional variance is a sum of a positive constant and the square of an inhomogeneous linear combination of past observations. Necessary and sufficient conditions for the existence of a stationary solution with finite variance are obtained. We give conditions under which the stationary solution with infinite fourth moment can exhibit long memory, the leverage effect, and a Lévy-stable limit behavior of partial sums of squares.

Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift

1986 ◽  
Vol 18 (04) ◽  
pp. 865-879 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Random Walks ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Partial Sums ◽  
Exit Times ◽  
First Passage ◽  
Partial Sum ◽  
Positive Expectation ◽  
Necessary And Sufficient

Consider the sequence of partial sums of a sequence of i.i.d. random variables with positive expectation. We study various random quantities defined by the sequence of partial sums, e.g. the time at which the first or last crossing of a given level occurs, the value of the partial sum immediately before or after the crossing, the minimum of all partial sums. Necessary and sufficient conditions are given for the existence of moments of these quantities.

XI.—On Unconditional Convergence in Topological Vector Spaces

1969 ◽  
Vol 68 (2) ◽  
pp. 145-157 ◽  
Author(s):  
A. P. Robertson
Keyword(s):  
Sufficient Conditions ◽  
Direct Proof ◽  
Vector Spaces ◽  
Unconditional Convergence ◽  
Partial Sums ◽  
Locally Convex Spaces ◽  
Topological Groups ◽  
Topological Vector Spaces ◽  
Necessary And Sufficient ◽  
Locally Convex

SynopsisFor a series of elements of a topological vector space, necessary and sufficient conditions are found, in terms of the set of finite partial sums, for unconditional convergence and for the corresponding Cauchy condition. The extent to which these results remain valid for topological groups is investigated. A new and direct proof, for locally convex spaces, is given of the theorem of Orlicz.

scholarly journals On Fully-Convex Harmonic Functions and their Extension

2018 ◽  
Vol 38 (2) ◽  
pp. 51-60
Author(s):  
Shahpour Nosrati ◽  
Ahmad Zireh
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Circular Arc ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Convex Univalent Functions

‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎.

scholarly journals Fourier coefficients and growth of harmonic functions

1987 ◽  
Vol 10 (3) ◽  
pp. 443-452 ◽  
Author(s):  
A. fryant ◽  
H. Shankar
Keyword(s):  
Harmonic Functions ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Several Variables ◽  
Order And Type ◽  
Necessary And Sufficient

We consider Harmonic Functions,Hof several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so thatHis an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in caseHis not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in caseHis entire or non-entire.

Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift

1986 ◽  
Vol 18 (4) ◽  
pp. 865-879 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Random Walks ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Partial Sums ◽  
Exit Times ◽  
First Passage ◽  
Partial Sum ◽  
Positive Expectation ◽  
Necessary And Sufficient

Consider the sequence of partial sums of a sequence of i.i.d. random variables with positive expectation.We study various random quantities defined by the sequence of partial sums, e.g. the time at which the first or last crossing of a given level occurs, the value of the partial sum immediately before or after the crossing, the minimum of all partial sums. Necessary and sufficient conditions are given for the existence of moments of these quantities.

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