scholarly journals Applications of Mittag-Leffer Type Poisson Distribution to a Subclass of Analytic Functions Involving Conic-Type Regions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Wali Khan Mashwani ◽  
Sama Arjika ◽  
...  
Keyword(s):  
Poisson Distribution ◽  
Analytic Functions ◽  
Convex Combination ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Properties ◽  
Distortion Bounds ◽  
Janowski Functions ◽  
Necessary And Sufficient

In this article, we introduce a new subclass of analytic functions utilizing the idea of Mittag-Leffler type Poisson distribution associated with the Janowski functions. Further, we discuss some important geometric properties like necessary and sufficient condition, convex combination, growth and distortion bounds, Fekete-Szegö inequality, and partial sums for this newly defined class.

scholarly journals Certain subclasses of analytic functions involving complex order

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 115-122 ◽  
Author(s):  
T.N. Shanmugam ◽  
S. Sivasubramanian ◽  
B.A. Frasin
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Order ◽  
Necessary And Sufficient ◽  
Class Of Functions

In the present investigation, we consider an unified class of functions of complex order. Necessary and sufficient condition for functions to be in this class is obtained. The results obtained in this paper generalizes the results obtained by Srivastava and Lashin [10], and Ravichandran et al. [4]. .

scholarly journals ON A CLASS OF CERTAIN ANALYTIC FUNCTIONS OF COMPLEX ORDER

1990 ◽  
Vol 21 (2) ◽  
pp. 101-109
Author(s):  
VINOD KUMAR ◽  
S. L. SHUKLA ◽  
A. M. CHAUDHARY
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Coefficient Estimate ◽  
Necessary And Sufficient Condition ◽  
Complex Order ◽  
Necessary And Sufficient ◽  
Radius Problem

We introduce a class, namely, $F_n(b,M)$ of certain analytic functions. For this class we detennine coefficient estimate, sufficient condition in terms of coefficients, maximization theonne concerning the coefficients, radius problem and a necessary and sufficient condition in terms of convolution. Our results generalize and correct some results of Nasr and Aouf ([2],[3]).

On the Modulii of Analytic Functions

1970 ◽  
Vol 13 (3) ◽  
pp. 325-327 ◽  
Author(s):  
Malcolm J. Sherman
Keyword(s):  
Analytic Functions ◽  
Point Of View ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Necessary And Sufficient Condition ◽  
Concrete Form ◽  
Norm Equality ◽  
Image Position ◽  
Necessary And Sufficient

The problem to be considered in this note, in its most concrete form, is the determination of all quartets f1, f2, g1, g2 of functions analytic on some domain and satisfying*where p > 0. When p = 2 the question can be reformulated in terms of finding a necessary and sufficient condition for (two-dimensional) Hilbert space valued analytic functions to have equal pointwise norms, and the answer (Theorem 1) justifies this point of view. If p ≠ 2, the problem is solved by reducing to the case p = 2, and the reformulation in terms of the norm equality of lp valued analytic functions gives no clue to the answer.

scholarly journals Regularization of distributions

1998 ◽  
Vol 21 (4) ◽  
pp. 625-636 ◽  
Author(s):  
Ricardo Estrada
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Boundary Values ◽  
Necessary And Sufficient Condition ◽  
Several Variables ◽  
Necessary And Sufficient ◽  
Harmonic And Analytic Functions ◽  
Regularization Of Distributions

We give a simple necessary and sufficient condition for the existence of distributional regularizations. Our results apply to functions and distributions defined in the complement of a point, in one or several variables. We also consider functions defined in the complement of a hypersurface. We apply these results to the existence of distributional boundary values of harmonic and analytic functions.

THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES

2001 ◽  
Vol 17 (4) ◽  
pp. 671-685 ◽  
Author(s):  
Hannes Leeb ◽  
Benedikt M. Pötscher
Keyword(s):  
Sufficient Conditions ◽  
Partial Sums ◽  
Stationary Processes ◽  
Sufficient Condition ◽  
Integrated Process ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.

scholarly journals Composition operators fromℬαtoQKtype spaces

2008 ◽  
Vol 6 (1) ◽  
pp. 88-104 ◽  
Author(s):  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Analytic Functions ◽  
Composition Operators ◽  
Nondecreasing Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Necessary And Sufficient

Suppose thatϕis an analytic self-map of the unit diskΔ. Necessary and sufficient condition are given for the composition operatorCϕf=fοϕto be bounded and compact fromα-Bloch spaces toQKtype spaces which are defined by a nonnegative, nondecreasing functionk(r)for0≤r<∞. Moreover, the compactness of composition operatorCϕfromℬ0toQKtype spaces are studied, whereℬ0is the space of analytic functions offwithf′∈H∞and‖f‖ℬ0=|f(0)|+‖f′‖∞.

scholarly journals Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1676
Author(s):  
Saeed Islam ◽  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Muhammad Arif ◽  
Ronnason Chinram
Keyword(s):  
Extreme Point ◽  
Point Theorem ◽  
Starlike Functions ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Sine Function ◽  
Necessary And Sufficient Condition ◽  
Closure Theorem ◽  
Necessary And Sufficient ◽  
Distortion Bound

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

scholarly journals a*-families of analytic functions

1984 ◽  
Vol 7 (3) ◽  
pp. 435-442 ◽  
Author(s):  
G. P. Kapoor ◽  
A. K. Mishra
Keyword(s):  
Analytic Function ◽  
Taylor Series ◽  
Analytic Functions ◽  
Extreme Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Family ◽  
Symmetric Points ◽  
Necessary And Sufficient

Using convolutions, a new family of analytic functions is introduced. This family, calleda*-family, serves in certain situations to unify the study of many previously well known classes of analytic functions like multivalent convex, starlike, close-to-convex or prestarlike functions, functions starlike with respect to symmetric points and other such classes related to the class of univalent or multivalent functions. A necessary and sufficient condition on the Taylor series coefficients so that an analytic function with negative coefficients is in ana*-family is obtained and sharp coefficents bound for functions in such a family is deduced. The extreme points of ana*-family of functions with negative coefficients are completely determined. Finally, it is shown that Zmorvic conjecture is true if the concerned families consist of functions with negative coefficients.

scholarly journals Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients II

2020 ◽  
Vol 28 (1) ◽  
pp. 85-103
Author(s):  
Waggas Galib Atshan ◽  
S. R. Kulkarni
Keyword(s):  
Fractional Derivative ◽  
Linear Combination ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Integral Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Derivative Operator ◽  
Necessary And Sufficient

AbstractIn this paper, we study a class of univalent functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z \right) + \gamma {z^2}\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)''}}} \right\} > \beta.A necessary and sufficient condition for a function to be in the class A_\gamma ^{\lambda,\mu,\nu}\left({n,\beta} \right) is obtained. Also, our paper includes linear combination, integral operators and we introduce the subclass A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right) consisting of functions with negative and fixed finitely many coefficients. We study some interesting properties of A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right).

Almost pseudo-Q-symmetric semi-Riemannian manifolds

2018 ◽  
Vol 15 (07) ◽  
pp. 1850117
Author(s):  
Ljubica Velimirović ◽  
Pradip Majhi ◽  
Uday Chand De
Keyword(s):  
Perfect Fluid ◽  
Curvature Tensor ◽  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Properties ◽  
Dust Fluid ◽  
Necessary And Sufficient ◽  
Fluid Spacetimes

The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider [Formula: see text]-spacetimes.

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