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The Normalized Miller-Ross Function And Its Geometric Properties, Khaled Mehrez
The Normalized Miller-Ross Function And Its Geometric Properties, Khaled Mehrez
Turkish Journal of Mathematics
The main objective of this paper is to study certain geometric properties (like univalence, starlikeness, convexity, close-to-convexity) for the normalized Miller-Ross function. The various results, which we have established in the present investigation, are believed to be new, and their importance is illustrated by several interesting consequences and examples. Furthermore, some of the main results improve the corresponding results available in the literature [15].
Some Properties Of Bazilevič Functions Involving Srivastava–Tomovski Operator, Daniel Breaz, Kadhavoor R. Karthikeyan, Elangho Umadevi, Alagiriswamy Senguttuvan
Some Properties Of Bazilevič Functions Involving Srivastava–Tomovski Operator, Daniel Breaz, Kadhavoor R. Karthikeyan, Elangho Umadevi, Alagiriswamy Senguttuvan
All Works
We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for starlikeness and Fekete–Szegö functional for functions belonging to the class.
Starlike Functions Of Complex Order With Respect To Symmetric Points Defined Using Higher Order Derivatives, Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan, Dharmaraj Mohankumar, Elangho Umadevi
Starlike Functions Of Complex Order With Respect To Symmetric Points Defined Using Higher Order Derivatives, Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan, Dharmaraj Mohankumar, Elangho Umadevi
All Works
In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.
An Application Of Modified Sigmoid Function To A Class Of $Q-$ Starlike And $Q-$ Convex Analytic Error Functions, Arzu Akgül
Turkish Journal of Mathematics
In this study, in the open unit disc $\Lambda$, by applying the $q-$ derivative operator and the fractional $q-$ derivative operator and by using the principle of subordination between analytic functions, we introduce some new interesting subclasses of $q-$ starlike and $q-$ convex analytic functions associated with error functions and modified sigmoid functions.
New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa
New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $T$ be the class of analytic functions in the open unit disc $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1.$ For $f(z)\in T,$ the Alexander integral operator $A_{-1}f(z),$ the Libera integral operator $L_{-1}f(z)$ and the Bernardi integral operator $B_{-1}f(z)$ were considered before. Using $A_{-1}f(z)$ and $L_{-1}f(z),$ a new integral operator $F_{\lambda}f(z)$ is considered. After discuss some properties of dominant for $F_{\lambda}f(z),$ another new integral operator $O_{-1}f(z)$ of $f(z)\in T$ is discussed. The object of the present paper is to discuss the dominant of new integral operators $F_{\lambda}f(z)$ and $O_{-1}f(z)$ concerning with some starlike functions and convex functions in $\mathbb{U}.$
Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations, Georgia Irina Oros
Univalence Criteria For Analytic Functions Obtained Using Fuzzydifferential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
Ever since Lotfi A. Zadeh published the paper "Fuzzy Sets" in 1965 setting the basis of a new theory named fuzzy sets theory, many scientists have developed this theory and its applications. Mathematicians were especially interested in extending classical mathematical results in the fuzzy context. Such an extension was also done relating fuzzy sets theory and geometric theory of analytic functions. The study begun in 2011 has many interesting published outcomes and the present paper follows the line of the previous research in the field. The aim of the paper is to give some references related to the connections already …
Some Applications Of Fractional Calculus For Analytic Functions, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
Some Applications Of Fractional Calculus For Analytic Functions, Nesli̇han Uyanik, Shi̇geyoshi̇ Owa
Turkish Journal of Mathematics
For analytic functions $f\left( z\right) $ in the class $A_{n},$ fractional calculus (fractional integrals and fractional derivatives) $D_{z}^{\lambda }f\left( z\right) $ of order $\lambda $ are introduced. Applying $% D_{z}^{\lambda }f\left( z\right) $ for $f\left( z\right) \in A_{n},$ we introduce the interesting subclass $A_{n}\left( \alpha _{m},\beta ,\rho ,\lambda \right) $ of $A_{n}.$ The object of this paper is to discuss some properties of $f\left( z\right) $ concerning $D_{z}^{\lambda }f\left( z\right) .$
On Differential Subordination Theorems Of Analytic Multivalent Functions Defined By Generalized Integral Operator, Waggas Galib Atshan, Ali Hussein Battor, Abeer Farhan Abaas
On Differential Subordination Theorems Of Analytic Multivalent Functions Defined By Generalized Integral Operator, Waggas Galib Atshan, Ali Hussein Battor, Abeer Farhan Abaas
Al-Qadisiyah Journal of Pure Science
In this paper, we obtain some applications of second order differential Subordination results involving a generalized integral operator for certain normalized analytic functions.
Differential Sandwich Resultsfor Univalent Functions, Waggas Galib Atshan, Haneen Zaghir Hassan
Differential Sandwich Resultsfor Univalent Functions, Waggas Galib Atshan, Haneen Zaghir Hassan
Al-Qadisiyah Journal of Pure Science
In the present paper, we obtain some subordination and superordination Results involving the integral operator for certain normalized analytic functions in the open unit disk. These results are applied to obtain sandwich results.
On Differential Subordination And Superordination Results Of Multivalent Functions Defined By A Linear Operator, Waggas Galib Atshan, Haneen Zaghir Hassan
On Differential Subordination And Superordination Results Of Multivalent Functions Defined By A Linear Operator, Waggas Galib Atshan, Haneen Zaghir Hassan
Al-Qadisiyah Journal of Pure Science
In this paper, we derive some results for multivalent analytic functions defined by linear operator by using differential Subordination and superordination
The Special Atom Space And Haar Wavelets In Higher Dimensions, Eddy Kwessi, G. De Souza, N. Djitte, M. Ndiaye
The Special Atom Space And Haar Wavelets In Higher Dimensions, Eddy Kwessi, G. De Souza, N. Djitte, M. Ndiaye
Mathematics Faculty Research
In this note, we will revisit the special atom space introduced in the early 1980s by Geraldo De Souza and Richard O'Neil. In their introductory work and in later additions, the space was mostly studied on the real line. Interesting properties and connections to spaces such as Orlicz, Lipschitz, Lebesgue, and Lorentz spaces made these spaces ripe for exploration in higher dimensions. In this article, we extend this definition to the plane and space and show that almost all the interesting properties such as their Banach structure, Hölder's-type inequalities, and duality are preserved. In particular, dual spaces of special atom …
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar
Turkish Journal of Mathematics
In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \(a,b\), and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \(\alpha=2^{-r}\) and order \(\alpha=2^{-r}\) type $\beta=2^{-1}$, with $r$ is a positive integer.
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak
Turkish Journal of Mathematics
This scientific investigation deals with introducing certain basic information relating to the error functions in z-plane, establishing extensive relations between various series expansions of the complex error functions and presenting a number of their implications.
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Turkish Journal of Mathematics
In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.
Coefficient Estimates For A New Subclasses Of Λ-Pseudo Biunivalent Functions Withrespect To Symmetrical Points Associated With The Horadam Polynomials, Adnan Alamoush
Turkish Journal of Mathematics
In the present article, we introduce two new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points in the open unit disk U defined by means of the Horadam polynomials. For functions belonging to these subclasses, estimates on the Taylor -Maclaurin coefficients ja2j and ja3j are obtained. Fekete-Szegö inequalities of functions belonging to these subclasses are also founded. Furthermore, we point out several new special cases of our results.
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Turkish Journal of Mathematics
Let $(\beta_n)_{n\ge 2}$ be a sequence of nonnegative real numbers and $\delta$ be a positive real number. We introduce the subclass $\mathcal{A}(\beta_n,\delta)$ of analytic functions, with the property that the Taylor coefficients of the function $f$ satisfies $\sum_{n\ge2}^{\infty}\beta_n a_n \le \delta$, where $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. The class $\mathcal{A}(\beta_n,\delta)$ contains nonunivalent functions for some choices of $(\beta_n)_{n\ge 2}$. In this paper, we provide some general properties of functions belonging to the class $\mathcal{A}(\beta_n,\delta)$, such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. …
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $\mathcal{A}(n)$ be the class of functions $$f(z)=a_nz^n + a_{n+1}z^{n+1}+\cdots (n\in \mathbb{N}),$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $f(z)\in \mathcal{A}(n)$, Miller and Mocanu in 1978 showed a very interesting result for $f(z)$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.
Coefficient Estimates For A Class Containing Quasi-Convex Functions, Osman Altintaş, Öznur Özkan Kiliç
Coefficient Estimates For A Class Containing Quasi-Convex Functions, Osman Altintaş, Öznur Özkan Kiliç
Turkish Journal of Mathematics
In the present study, we introduce the classes $\mathcal {Q_{CV}}\left(\mu, A,B \right)$ and $\mathcal{Q_{ST}}\left(\eta, A,B \right)$. Furthermore, we obtain coefficient bounds of these classes.
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Some Subclasses Of Analytic Functions Of Complex Order, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.
Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi
Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi
MSU Graduate Theses
A large number of infinite sums, such as , cannot be found by the methods of real analysis. However, many of them can be evaluated using the theory of residues. In this thesis we characterize several methods of summations using residues, including methods integrating residues and the Bernoulli numbers. In fact, with this technique we derive some summation formulas for particular Finite Sums and Infinite Series that are difficult or impossible to solve by the methods of real analysis.
Birkhoff–James Orthogonality And The Zeros Of An Analytic Function, Raymond Cheng, Javad Mashreghi, William T. Ross
Birkhoff–James Orthogonality And The Zeros Of An Analytic Function, Raymond Cheng, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space ℓp with p ∈ (1,∞), along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.
Strong Differential Subordination, Georgia Irina Oros, Gheorghe Oros
Strong Differential Subordination, Georgia Irina Oros, Gheorghe Oros
Turkish Journal of Mathematics
The concept of differential subordination was introduced in [4] by S. S. Miller and P. T. Mocanu and the concept of strong differential subordination was introduced in [1] by J. A. Antonino and S. Romaguera. This last concept was applied in the special case of Briot-Bouquet strong differential subordination. In this paper we study the strong differential subordinations in the general case, following the general theory of differential subordinations presented in [4].