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The primary goal of this paper is to introduce and investigate a novel subclass of analytic functions in the open unit disk by generalizing the Srivastava-Attiya operator. So by using the generalization we have introduced a subclass of analytic function with negative coefficients in the unit disk. We have referred to the previous studies that used the Sirvastava-Attiya operator and generalized it, explained the functions of the class 퓐 and the basic definitions that included this paper. We used some important lemmas from previous studies to prove our results, and we obtained some important geometric properties of the analytical functions. We proved the theorem of growth and destortion, and we showed the cofficient bound, extreme points of the functions in this class, in addition to the radii of the starlike, convex and close-to-convex functions of order 휑. Finally, we defined the 훼 −neighborhood and showed the relationship between the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ (γ , ρ , l , σ) and the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ , ω (γ , ρ , l , σ). [ABSTRACT FROM AUTHOR]

One of the important problems of potential theory is the study of (sub) harmonicity of separately (sub) harmonic functions. This problem has been studied by many authors and fairly complete results have been obtained. In this paper we will give a survey of results in this area and study a → -separately subharmonic functions. In this paper, we assume that all coefficients of differential forms belong to the class С1, unless additional smoothness conditions are required. We give a definition of Λ-separately subharmonic function, where Λ=(α′,α″) and we show that under additional conditions, these functions belongs to the class α-subharmonic functions, where a = a ′ (z) ∧ a ′ ′ (w) ∧ β , β = d d c ( | z | 2 + | w | 2). If the function u(z, w)∈С2 (D × G) is ∧−separately subharmonic, then by the set of variables ddcu(z, w) ∧α(z, w) ≥0, i.e. the function u(z, w) is α-subharmonic, where a (z , w) = a ′ (z) ∧ a ′ ′ (w) ∧ β , β = d d c ( | z | 2 + | w | 2). If a function u (z, w), (z, w) ∈ D×G is Λ-separately harmonic and coefficients of differential forms α′(z) and α″(w) are real analytic in the domains D and G respectively, then u(z, w) is real analytic α−harmonic function (where α=α′(z) ∧α″(w)∧β) in the domain D×G by the set of variables. [ABSTRACT FROM AUTHOR]

We consider A(z)−analytic functions in case when A(z) is anti-analytic function. This article introduces Lp classes of A(z)−analytics functions by p ≥ 1. In this paper, we introduce for a non-tangential boundary value of the A(z)−analytic function. Thus, this paper proves Fatou's theorem on non-tangential values for A(z)−analytic functions. [ABSTRACT FROM AUTHOR]

In this paper, a new operator was defined μ m , k j. v f (w)) : A → A. Associated with Hadamard product of the Komatu Integral operator [MATH] and the Dziok-Srivastava operator [MATH]. And done use the method of differential subordination to derive certain properties of the differential operator μ m , k j. v f (w)). And aim of this paper is to use the relation (α 1 k + 1) μ m , k j + 1 , v f (w) = w (μ m , k j , v f (w)) ' + α 1 k (μ m , k j , v f (w)) [ABSTRACT FROM AUTHOR]

We denote by A the class of all univalent and analytic functions f (z) = z + Σ k = 2 ∞ a k z k in the open unit disk 픻={z∶ |z|<1}. Here, the classes with respect to all functions in A that are univalent in 픻 are further represented by S. There is an inverse f−1 for each function f∈S. If both f and its inverse g=f−1 are univalent, then, a function f∈A is called bi-univalent in 픻. Results for covering theorem, distortion theorem, rotation theorem, growth theorem, as well as the convexity radius with respect to the functions of the class Σ of bi-univalent functions that are connected to a generalised differential operator D λ , a s , m , k f (z) , are obtained in this paper. In order to get the desired results, we utilised the elementary transformations where the class Σ is preserved. Subsequently, the theorems of the required properties of bi-univalent functions are attained. These results can be reduced to other previous well-known findings by assigning different initial coefficient |a2|. [ABSTRACT FROM AUTHOR]

In this paper, we aim to define a subclass of bi-univalent functions involving Chebyshev polynomials of the second kind. Furthermore, we will find the first two initial coefficients and Fekete-Szegö inequality for the newly defined subclass. Several new corollaries and consequences will be presented. [ABSTRACT FROM AUTHOR]

The investigation of operators is significant in mathematics, particularly in geometric function theory. Operators have generated a considerable amount of attention in the theory of geometric functions because of their significance in generalising and preserving subclasses of analytic univalent functions. Many mathematicians have discussed operators and the new generalisation in various articles. Research on operators has been conducted since 1915. Since then, mathematicians are still very interested in discussing operators with many properties of analytic univalent functions. Hence, this paper introduces a new generalised operator D λ , α s , m , k f (z) of analytic functions in the open unit disc using the generalised Srivastava-Attiya operator, generalised Al-Oboudi operator, and binomial series. Based on this new operator, some subclasses are defined using differential subordinations method. Furthermore, the inclusion properties are obtained for functions in these subclasses. [ABSTRACT FROM AUTHOR]

In the paper multiplicative polynomials and analytic functions on Fréchet algebras are investigated. Some connections with homomorphisms on symmetric tensor products of the Fréchet algebras are obtained. A method of constructing of multiplicative G-analytic mapping on Fréchet algebras is proposed. [ABSTRACT FROM AUTHOR]

In this paper, we studied a new subclass of analytic univalent functions defined by differ – integral operator. We obtain coefficients estimates radii of closed – to – convex and some closure theorems of this subclass. [ABSTRACT FROM AUTHOR]

In this paper ,we define new subclasses B e, τ q (δ , η , ϑ) , E y q (ξ , ϑ) and D σ q (λ , ϑ) of analytic function in open unit disc with f on quasi-subordination, determine the initial coefficient estimates |a2| and |a3| and determine coefficient | a 3 − μ a 2 2 | in equalities. We discuss the improved results for the associated classes involving subordination and majorization results briefly. [ABSTRACT FROM AUTHOR]

In this paper we studied Fredholm weighted tensor sum operators on weighted Banach spaces of Holomorphic functions and on the smaller spaces. Also we characterized of Fredholm tensor sum operators and for a general typical weight function. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss the third-order differential subordination and the corresponding differential superordination problems by using derivative operator F T η , ν , ϱ β f (z) . Some classes of admissible functions are obtained and the third-order differential sandwich-type outcomes are presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the class of the analytic functions called ℘ and to investigate the various properties of the functions belonging this class. We present a different version of Schwarz Lemma and some inequalities related to the angular derivative. [ABSTRACT FROM AUTHOR]

In this paper, a new class of analytic and univalent functions in the open unit disk using Bessel function is defined. Some geometric properties likes, coefficient, distortion result, extreme point and Fekete-SzegÖ inequality are studied for this class. [ABSTRACT FROM AUTHOR]

We find sharp estimates of the Hankel determinant H2,2 and Zalcman functional J2,3 over the class CV of analytic functions f normalised such that Re (1 − z) 2 f ' (z) > 0 for U={z ∈ C:|z|<1}. i.e, the subclass of the class of functions convex in one direction and the function Re [ (1 − α) f (z) z + α f ' (z) ] > 0 in the class R(α) [ABSTRACT FROM AUTHOR]

We study different presentations of the symmetric group S∞ of all bijections of the set of natural numbers ℕ on the spaces l 1 ⊗ ^ l 1 , l 1 ⊗ ^ s l 1 and corresponding algebras of symmetric analytic functions on these spaces. [ABSTRACT FROM AUTHOR]

This report introduces the basic notion. For some normalized analytic functions described in the open unit disc, we establish certain subordination and superordination results involving operator R α , β m , k defined by the Mittag-Leffler function. In order to determine sandwich outcomes, these results are applied. [ABSTRACT FROM AUTHOR]

In this article, we give some results and properties of the differential subordination and superordination in the third-order for univalent functions in the open unit disk U Incorporating a generalized multiplier operator J α , γ μ f (v) . The findings are obtained by examining relevant classes of admissible functions. Also, some sandwich theories will be noted. [ABSTRACT FROM AUTHOR]