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NORMALIZED DINI FUNCTIONS CONNECTED WITH k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS
ECE, SADETTIN,EKER, SEVTAP SUMER,SEKER, BILAL The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.5
The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.
GEOMETRIC PROPERTIES ON (j, k)-SYMMETRIC FUNCTIONS RELATED TO STARLIKE AND CONVEX FUNCTION
Gochhayat, Priyabrat,Prajapati, Anuja Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST<sub>[j,k]</sub>(A, B) and K<sub>[j,k]</sub>(A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a<sup>2</sup><sub>3</sub> - a<sub>5</sub>|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST<sub>[j,k]</sub>. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K<sub>[j,k]</sub>(α) for all 0 ≤ α < 1.
JANOWSKI STARLIKENESS AND CONVEXITY
KANIKA KHATTER,V. Ravichandran,S. SIVAPRASAD KUMAR 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4
Certain necessary and sufficient conditions are determined for the functions f(z) = z - P1 n=2 anzn, an ≥ 0, defined on the open unit disk, to belong to various subclasses of starlike and convex func- tions. Also discussed are certain sufficient conditions for the normalised analytic functions f of the form (z=f(z))μ = 1 + P1 n=1 bnzn, μ ∈ C to belong to the class of Janowski starlike functions.
Starlikeness and convexity of fractional calculus operators
Choi, Jae Ho,KIM, Yong Chan,Srivastava, H.M. 경북대학교 위상수학 기하학연구센터 1999 硏究論文集 Vol.7 No.-
The main object of the present paper is to investigate the starlikeness and convexity of certain general families of operators of fractional calculus (that is, fractional integral and fractional derivative). Relevant connections are also pointed out with various earlier results involving these subclasses of analytic functions.
G. Murugusundaramoorthy,N. Magesh 장전수학회 2007 Proceedings of the Jangjeon mathematical society Vol.10 No.2
Making use of the generalized hypergeometric functions, we introduce some generalized class of k−uniformly convex and starlike functions and for this class, we obtain several interesting subordination results. In particular, we obtain subordination results for various classes of uniformly convex and starlike functions. Our result includes as special cases.
ON UNIVALENT SUBORDINATE FUNCTIONS
Park, Suk-Joo Korean Society of Mathematical Education 1996 純粹 및 應用數學 Vol.3 No.2
Let $f(z)=z+\alpha_2 z^2$+…+ \alpha_{n}z^n$+… be regular and univalent in $\Delta$ = {z : │z│<1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.
THE THIRD HERMITIAN-TOEPLITZ AND HANKEL DETERMINANTS FOR PARABOLIC STARLIKE FUNCTIONS
Rosihan M. Ali,Sushil Kumar,Vaithiyanathan Ravichandran 대한수학회 2023 대한수학회보 Vol.60 No.2
A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.
Saliu Afis,Kanwal Jabeen,Semiu Oladipupo Oladejo,Olaide Yetunde Saka-Balogun 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
In this present work, we inaugurated subclasses of analytic functions which are associated with generalized Mittag Leffler Functions. Inclusion implications and integral preserving properties under the Bernardi integral operator are investigated. Some consequences of these findings are also illustrated.
K. Vijaya,G. Murugusundaramoorthy,N. E. Cho 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.1
The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.
GEOMETRIC PROPERTIES OF GENERALIZED DINI FUNCTIONS
Deniz, Erhan,Goren, Seyma The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.