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In this article, our aim is to study analytic functions related with Salagean operator and associated with the right half of the lemniscate of Bernoulli. We find the estimates of the third Hankel determinant for new family of analytic functions. It is important to mention that our results generalize a number of existence results in the literature.

In this article, we study the Fekete-Szegö functional associated with a new class of analytic functions related to the class of bounded turning by using the principle of quasi-subordination. We derived the coefficient estimates including the classical Fekete-Szegö inequality for functions belonging to this class. We also improved some existing results.

This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing q−Ultraspherical polynomials under q−Saigo’s fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we define a Bernardi type quantum integral operator. It transforms the starlike univalent in the unit disk into a starlike region in it. We show that the upper-bound of the third-order Hankel determinant for classes of q-starlike functions is connected with a q-analogue integral operator, defined by a modified q-Bernardi integral operator. The Fekete-Szegö inequality of these classes is also investigated. Numerous well-known specific instances, examples and graphics are listed in the paper. The computations are done by Mathematica 13.3. [ABSTRACT FROM AUTHOR]

We define a differential operator for analytic functions of fractional power. A class of analytic functions containing this operator is studied. Finally, we determine conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning.

In this article, we introduce and study a new q-fractional integral operator which essentially stems from a successive application of the Srivastava-Owa operator of fractional integration with the q-Ruscheweyh derivative operator. As an application of this new q-fractional integral operator, we investigate a coefficient problem involving the second Hankel determinant H²2(f) for normalized analytic and univalent functions f(z) belonging to some normalized families of q-starlike and q-convex functions in the open unit disk U. [ABSTRACT FROM AUTHOR]

We establish a new class of uniformly starlike functions by using a differential operator that was motivated by the authors. Moreover, we introduce a subclass with negative coefficients by fixing a second coefficient. Furthermore, we discuss the closure of this subclass under convex combinations. Finally, we investigate the extreme point values for the new class. [ABSTRACT FROM AUTHOR]

Quantum theory has many applications in mathematics, particularly in the study of special functions and quantum physics. In this article, based on the concept of Lemniscate of Bernoulli, we provide q-Lemniscate of Bernoulli (x² + y²) - 2(x² - y²) = q² -1. The q-Lemniscate Bernoulli is used to define a new class of analytic functions using a quantum difference operator, and for this class, an upper bound Fekete-Szegö problems and the second Hankel determinant are studied. Furthermore, several known cases with proven findings are presented. In addition, by using the Ruscheweyh q-differential operator, certain useful applications of the main findings are attained. [ABSTRACT FROM AUTHOR]

By making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk 𝕌 = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.