No abstract

Inequalities play a fundamental role in many branches of mathematics and particularly in real analysis. By using inequalities, we can find extrema, point of inflection, and monotonic behavior of real functions. Subordination and quasisubordination are important tools used in complex analysis as an alternate of inequalities. In this article, we introduce and systematically study certain new classes of meromorphic functions using quasisubordination and Bessel function. We explore various inequalities related with the famous Fekete-Szego inequality. We also point out a number of important corollaries.

In this paper, we introduce and investigate a new subclass of bi-univalent functions related with generating function of Gegenbauer polynomials. We will mainly find bounds on Maclaurin series coefficients for functions belonging to this class. We also study the famous Fekete-Szegö type problem for this subclass which is obtained. We will also point out many special cases as corollaries.

<abstract><p>In this paper, we will discuss some generalized classes of analytic functions related with conic domains in the context of $ q $-calculus. In this work, we define and explore Janowski type $ q $-starlike functions in $ q $ -conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness, growth and distortion results for these classes. It is important to mention that our results are generalization of number of existing results.</p></abstract>

In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.