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In this article, we introduce two new classes of analytic functions Jtanh and JSG which are associated with the activation functions and defined by the ratio of analytic representations of convex and starlike functions. For functions in these classes, our primary goal is to determine the sharp upper bounds of second and third Hankel determinants.

In this article, the present study employs the utilization of the concepts pertaining to (x,y)-symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into the examination of convolution properties, which serve as a tool for investigating and inferring adequate and equivalent conditions. Moreover, we also explore specific characteristics of the class S˜qx,y(α,β,λ), thereby further scrutinizing the convolution properties of these newly defined classes.

This study describes the synthesis, characterization, and biological activities of halogenated xanthone, 3-O substituted xanthone, and prenylated xanthone derivatives. The molecular structures of these compounds were identified using 1H NMR, 13C NMR, 2D NMR, FTIR and DIMS. All synthesized compounds were evaluated against two cancer cell lines: breast adenocarcinoma MCF-7 and MDA-MB-231 by application of the MTT assay. With this approach, xanthones 9 and 13 were identified as putative aromatase activating agents through the inhibition of interactions with MCF-7 and MDA-MB-231. The selected compounds, 9 and 13, were further examined for toxicity against the African Green Monkey Kidney cell (VERO) and Non-tumorigenic Lung Epithelial cell lines (BEAS-2B). In addition, in-silico docking studies were conducted to estimate the binding poses and residues implicated in probable MCF-7 and MDA-MB-231 interactions.

One of the challenging tasks in the study of function theory is how to obtain sharp estimates of coefficients that appear in the Taylor–Maclaurin series of analytic univalent functions, and for obtaining these bounds, researchers used the concepts of Carathéodory functions. Among these coefficient-related problems, the problem of the third-order Hankel determinant sharp bound is the most difficult one. The aim of the present study is to determine the sharp bound of the Hankel determinant of third order by using the methodology of the aforementioned Carathéodory function family. Further, we also study some other coefficient-related problems, such as the Fekete–Szegő inequality and the second-order Hankel determinant. We examine these results for the family of bounded turning functions linked with a cardioid-shaped domain.

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of conformal maps. The primary goal of this paper was to calculate the sharp estimates of the initial coefficients and some of their combinations (the Hankel determinants, Zalcman’s functional, etc.) for the class of symmetric starlike functions linked with the sigmoid function. Moreover, we also determined the bounds of second-order Hankel determinants containing coefficients of logarithmic and inverse functions of the same class.

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass SQ of analytic functions with f′(z) subordinated to 1/(1−z)2 in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant H2,3f and the third Hankel determinant H3,1f for f∈SQ. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions.

One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some sharp estimates of problems involving coefficients for the family of convex functions with respect to symmetric points and associated with a hyperbolic tangent function. These problems include the first four initial coefficients, the Fekete–Szegö and Zalcman inequalities, and the second-order Hankel determinant. Additionally, the inverse and logarithmic coefficients of the functions belonging to the defined class are also studied in relation to the current problems.

Some geometric properties of a certain univalent function in the unit disk are considered in this work and the results extend some known results in the literature.

Abstract New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to figure out twenty-seven forms of exact solutions, which are soliton, rational, and periodic ones. Also, for some suitable values of parameters, the exact solutions are found, namely dark, bell type, periodic, soliton, singular soliton, and several others, by using the conformable derivative. These types of solutions have not been proclaimed so far. 2D and 3D graphical patterns of some solutions are also given for clarification of physical features. The conformable derivative is one of the excellent choices to solve the nonlinear conformable problems arising in theory of solitons and many other areas. The results are new and very interesting for the large community of researchers working in the field of mathematics and mathematical physics.

In this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. Some existing classical methods such as the Newton method, Halley method, and Traub's approach and their various modified forms are the special cases of these newly purposed schemes. These new iterative schemes are a good addition in existing methods and are also a comprehensive and generalized form for finding the solution of nonlinear equations.

Various problems of pure and applied sciences can be studied in the unified framework of nonlinear equations. In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proven. For the implementation and performance of the new methods, some examples are solved and the results are compared with some existing methods.

The main concern is to explore an electro-magneto hydrodynamic (EMHD) squeezing flow of Ag-Fe3O4H2O hybrid nanofluid between stretchable parallel Riga plates. The benefits of the use of hybrid nanofluids, and the parameters associated to it, have been analyzed mathematically. This particular problem has a lot of importance in several branches of engineering and industry. Heat and mass transfer along with nonlinear thermal radiation and chemical reaction effects have also been incorporated while carrying out the study. An appropriate selection of dimensionless variables have enabled us to develop a mathematical model for the present flow situation. The resulting mathematical method have been solved by a numerical scheme named as the method of moment. The accuracy of the scheme has been ensured by comparing the present result to some already existing results of the same problem, but for a limited case. To back our results further we have also obtained the solution by anther recipe known as the Runge-Kutta-Fehlberg method combined with the shooting technique. The error analysis in a tabulated form have also been presented to validate the acquired results. Furthermore, with the graphical assistance, the variation in the behavior of the velocity, temperature and concentration profile have been inspected under the action of various ingrained parameters. The expressions for skin friction coefficient, local Nusselt number and local Sherwood number, in case of Ag-Fe3O4H2O hybrid nanofluid, have been derived and the influence of various parameters have also been discussed.

The object of the present paper is to investigate a family of integral operators defined on the space of meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex meromorphic functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Several interesting integral-preserving properties are also considered.

We study univalence properties for certain subclasses of univalent functions K, K2, K3, and S(p), respectively. These subclasses are associated with a generalized integral operator. The extended Becker-typed univalence criteria will be studied for these subclasses.