Subclasses Of Functions Research Articles

An Extended Subclass of Meromorphic Multivalent Functions Involving Ruscheweyh Derivative Operator

     In this paper, we introduce and discuss an extended subclass〖 Ą〗_p^*(λ,α,γ) of meromorphic multivalent functions involving Ruscheweyh derivative operator. Coefficients inequality, distortion theorems, closure theorem for this subclass are obtained.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions Linked with Lucas-Balancing Polynomials

We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also discussed. Along with presenting some new results, we also explore pertinent connections to earlier findings.

Envy-free relaxations for goods, chores, and mixed items

In fair division problems, we are given a set S of m items and a set N of n agents with individual preferences, and the goal is to find an allocation of items among agents so that each agent finds the allocation fair. There are several established fairness concepts and envy-freeness is one of the most extensively studied ones. However envy-free allocations do not always exist when items are indivisible and this has motivated relaxations of envy-freeness: envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) are two well-studied relaxations. We consider the problem of finding EF1 and EFX allocations for utility functions that are not necessarily monotone, and propose four possible extensions of different strength to this setting.In particular, we present a polynomial time algorithm for finding an EF1 allocation for two agents with arbitrary utility functions. An example is given showing that EFX allocations need not exist for two agents with non-monotone, non-additive, identical utility functions. However, when all agents have monotone (not necessarily additive) identical utility functions, we give a pseudo-polynomial time algorithm that always finds an EFX allocation of chores. As a step toward understanding the general case, we discuss two subclasses of utility functions: Boolean utilities that are {0,+1}-valued functions, and negative Boolean utilities that are {0,−1}-valued functions. For the latter, we give a polynomial time algorithm that finds an EFX allocation when the utility functions are identical.

Fekete-Szegӧ Functional for Classes X_q^n (φ) and Y_q^n (φ)

Two new subclasses of analytic functions are proposed by applying q-differential operator which is denoted as . Throughout this study, we acquired the initial coefficients  and  and the upper bound for the functional   of the functions  in the classes  and .

Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions

Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions

Some properties of subclass of multivalent functions associated with a generalized differential operator

In this paper, the new subclass Sb,λ,δ,pn(α)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}^n_{b,\\lambda ,\\delta ,p} ({\\alpha })$$\\end{document} of a linear differential operator’s Nλ,δ,pnf(ζ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}_{\\lambda ,\\delta ,p}^{n}f(\\zeta )$$\\end{document} associated with multivalent analytical function has been introduced. Further, the coefficient inequalities, extreme points for the extremal function, sharpness of the growth and distortion bounds, partial sums, starlikeness, and convexity of the subclass is investigated.

On a Class of Multivalent Functions with Negative Coefficients Involving (r, q)− Calculus

In this research, we focused on presenting a novel subclass of multivalent analytic functions situated in the open unit disk, characterized by the use of Jackson’s derivative operator. Our investigation systematically establishes the requisite inclusion conditions in this class, offering detailed coefficient characterizations. The exploration encompasses an array of significant properties intrinsic to this subclass, encompassing coefficient estimates, growth and distortion theorems, identification of extreme points, and the determination of the radius of starlikeness and convexity for functions falling within this specialized category. Expanding the preliminary findings, this research extended the inquiry to delve deeper into the intriguing features and implications associated with this new subclass of multivalent analytic functions. The research concentrated the light on the nuanced intricacies of coefficient estimates, providing a comprehensive understanding of how these functions evolve within the open unit disk through exploring the growth and distortion theorems, unraveling the underlying mathematical principles governing the behavior of functions in this subclass as they extend beyond the unit disk. The findings of this research contribute to the broader understanding of multivalent analytic functions, paving the way for further exploration and applications in diverse mathematical contexts.

On some classes of multiplicative functions

AbstractAn arithmetical function f is multiplicative if $$f(1)=1$$ f ( 1 ) = 1 and $$f(mn)=f(m)f(n)$$ f ( m n ) = f ( m ) f ( n ) whenever m and n are coprime. We study connections between certain subclasses of multiplicative functions, such as strongly multiplicative functions, over-multiplicative functions and totients. It appears, among others, that the over-multiplicative functions are exactly same as the totients and the strongly multiplicative functions are exactly same as the so-called level totients. All these functions satisfy nice arithmetical identities which are recursive in character.

Study of a generalized subclass of meromorphic functions

This paper is concerned with a new subclass of meromorphic close-to-convex functions defined by means of subordination. various properties of this class such as coefficient estimates, inclusion relationship, distortion property and radius of meromorphic convexity, are established. Some earlier known results follow as special cases.

Coefficient estimates for a subclass of bi-univalent functions associated with the Salagean differential operator

In this paper, we present and examine a novel subset of the function class ∑, which consists of analytic and bi-univalent functions defined in the open unit disk U and connected to the Salagean differential operator. Additionally, we determine estimates for the Taylor-Maclaurin coefficients |a2| and |a3| functions within this new subclass and enhance some recent findings. 2010 Mathematics Subject Classification. 30C45; 30C50.

On Certain Subclass of Meromorphic Multivalent Functions Associated with Fractional Calculus Operator

     In this paper, the class of meromorphic multivalent functions of the form by using fractional differ-integral operators is introduced. We get Coefficients estimates, radii of convexity and star likeness. Also closure theorems and distortion theorem for the class ,  is calculaed.

Estimates for a class of analytic and univalent functions connected with quasi-subordination

Geometric Function Theory, an active field of studied that has its roots in complex analysis, has gained an impressive attention from many researchers. This occurs largely because it deals with the study of geometric properties of analytic (and univalent) functions where many of its applications spread across many fields of mathematics, mathematical physics and engineering. Notable areas of application include conformal mappings, special functions, orthogonal polynomials, fluid flows in physics and engineering designs. The investigations in this paper are on a subclass of analytic and univalent functions defined in the unit disk Ω and denoted by Qaq(m). The definition of the new class encompasses some well-known subclasses of analytic and univalent functions such as the classes of starlike functions, Yamaguchi functions, and Ma-Minda functions. Two key mathematical principles involved in the definition of the class are the principles of Taylor’s series and quasi-subordination. Some of the investigations carried out on functions f ∈ Qaq(m) are however, the upper estimates for some initial bounds, the solution to the well-known Fekete-Szego problem and the upper estimate for a Hankel determinant.

Fekete-Szegö type functionals associated with certain subclasses of bi-univalent functions

In this article, we define and discuss some new subclasses of bi-univalent functions associated with Fibonacci numbers and shell-like curves. We estimate the first two Taylor-Maclaurin coefficients for functions belonging to these classes. We study the inequalities related with Fekete-Szegö type. Furthermore, we point out some corollaries related to existing result.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions linked with Horadam Polynomials

In this work, we investigate some subclasses of bi-univalent and regular functions associated with Horadam polynomials in the open unit disk $\mathfrak{U}=\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. For functions that belong to these subclasses, we find bounds on their initial coefficients. The functional problem of Fekete-Szegö is also examined. Along with presenting some new results, we also talk about pertinent connections to earlier findings.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions linked with Horadam Polynomials

In this work, we investigate some subclasses of bi-univalent and regular functions associated with Horadam polynomials in the open unit disk $\mathfrak{U}=\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. For functions that belong to these subclasses, we find bounds on their initial coefficients. The functional problem of Fekete-Szegö is also examined. Along with presenting some new results, we also talk about pertinent connections to earlier findings.

Generalized q-Srivastava-Attiya operator on multivalent functions

In this article, we define a generalized q-integral operator on multivalent functions. It generalizes many known linear operators in Geometric Function Theory (GFT). Inclusions results, convolution properties and q-Bernardi integral preservation of the subclasses of analytic functions are discussed. Mathematics Subject Classification (2010): 30C45, 30C80, 30H05. Received 29 March 2021; Accepted 26 July 2021

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

Various operators of fractional calculus, as well as their quantum (or q-) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant.

Fuzzy differential subordination associated with generalized Mittag-Leffler type Poisson distribution

This article introduces a new operator defined by the convolution of the Poisson distribution series and the generalized Mittag-Leffler function. Applying this operator, we study a novel subclass of analytic functions using the technique of fuzzy differential subordination. Also, we prove some significant results related to the fuzzy differential relation for this novel class. These results are applied to particular functions to showcase the significance of our findings.

A New Subclass of Analytic Functions Associated with the q-Derivative Operator Related to the Pascal Distribution Series

A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized.