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Register a new userSubclasses of meromorphically multivalent functions defined by a differential operator
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In this paper we introduce and study two new subclasses Sigma_{lambdamu mp}(alpha,beta)$ and $Sigma^{+}_{lambdamu mp}(alpha,beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.
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In the present paper the new multiplier transformations $mathrm{{mathcal{J}% }}_{p}^{delta }(lambda ,mu ,l)$ $(delta ,lgeq 0,;lambda geq mu geq 0;;pin mathrm{% }%mathbb{N} )}$ of multivalent functions is defined. Making use of the operator $mathrm{% {mathcal{J}}}_{p}^{delta }(lambda ,mu ,l),$ two new subclasses $mathcal{% P}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ and $widetilde{mathcal{P}}% _{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$textbf{ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $mathcal{P}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ and $widetilde{mathcal{P}}_{lambda ,mu ,l}^{delta }(A,B;sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.
The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic oscillator. In this paper, we define a symmetric $q$-derivative operator and study new family of univalent functions defined by use of that operator. We establish some new relations between functions satisfying analytic conditions related to conical sections.
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fractional operators are illustrated.
Some differential implications of classical Marx-Strohhacker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential subordination which in turn, corrects the results of Selvaraj and Stelin [On multivalent functions associated with fixed second coefficient and the principle of subordination, Int. J. Math. Anal. {bf 9} (2015), no.~18, 883--895].
In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $kappa-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third coefficients) and Fekete - Szeg{o} inequalities. Also we discuss the special cases of the obtained results.
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