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Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function [PDF]
International Journal of Mathematics and Mathematical Sciences, 2014 By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new ...
K. AL-Shaqsi
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Mathematics, 2023 The notions of strong differential subordination and its dual, strong differential superordination, have been introduced as extensions of the classical differential subordination and superordination concepts, respectively.
Alina Alb Lupaş, Georgia Irina Oros
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Results of Third-Order Strong Differential Subordinations
AxiomsIn this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions.
Madan Mohan Soren +2 more
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Symmetry, 2023 The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and ...
F Ghanim, Alb Lupas Daciana Alina
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Strong differential subordination and superordination of analytic functions
Journal of Mathematical Analysis and Applications, 2012 Let \(A\) be the class of functions analytic in the unit disc \(\mathbb{U}= \{z\in\mathbb{C}:|z|< 1\}\). We say that a function \(f\in A\) is subordinate to \(g\in A\) if there exists a function \(w\in A\) such that \(|w(z)|< 1\) and \(f(z)= g(w(z))\) for \(z\in \mathbb{U}\). In this case we write \(f\prec g\) or \(f(z)\prec g(z)\).
Jeyaraman, M.P., Suresh, T.K.
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Strong Differential Subordination to Briot-Bouquet Differential Equations
Journal of Differential Equations, 1994 Two theorems are proved on differential subordination \[ p(z) + {zp'(z) \over z \bigl( f'(z)/f(z) \bigr) \bigl[ \alpha p(z) + \beta \bigr] } \prec g(z). \] In fact, \(p(z) \prec g(z)\) provided \(p\) is analytic in the unit disc \(D\), \(p(0) = c\), \(g\) is univalent in \(D\), \(f\) analytic in \(D\) such that \(z(f'(z)/f(z))\) is analytic and \(\neq ...
Antonino, J.A., Romaguera, S.
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STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR
Korean Journal of Mathematics, 2015 Summary: In this work, certain classes of admissible functions are considered. Some strong differential subordination and superordination properties of analytic functions associated with new generalized derivative operator \(\mathfrak{B}^{\mu,q,s}_{\lambda_1,\lambda_2,\ell,d}\) are investigated.
Maslina Darus
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Annals of Probability, 1995 If \(X\) and \(Y\) are a pair of discrete martingales, suppose the difference sequence of \(X\) satisfies a pointwise domination with the corresponding sequence of \(Y\). Then one says that \(X\) is differentially subordinate to \(Y\). In the continuous parameter case the concept is in terms of their quadratic variations. Thus if \(X = \{X_t, {\mathcal
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On special strong differential subordinations using multiplier transformation
Applied Mathematics Letters, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alb Lupas Daciana Alina
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Strong Differential Subordination and Stochastic Integration
Annals of Probability, 1994 Various sharp inequalities are established connecting the ``size'' of the stochastic integral \(Y= \int HdX\) and the ``size'' of a semimartingale integrator \(X\) for bounded predictable integrands \(H\). The proofs are mainly based on adequate choice of special functions related to some boundary value problems.
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