Multiplier Transformations Research Articles

Sandwich theorems involving fractional integrals applied to the $ q $ -analogue of the multiplier transformation

<abstract><p>In this paper, the research discussed involves fractional calculus applied to a $ q $-operator. Fractional integrals applied to the $ q $-analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research.</p></abstract>

Multiplier transformation of E-commerce to S-commerce in emerging economy

Relevance. Electronic commerce (e-commerce) and social commerce (s-commerce) are transforming business and consumer behaviour in Southeast Asia, propelled by digital advancements and increased internet and smartphone usage. This trend is significantly influencing economic growth and market dynamics in these emerging economies. Research Objective. This study aims to perform a comparative analysis of e-commerce and s-commerce across Southeast Asian countries. Additionally, it seeks to explore the evolution from e-commerce to s-commerce in emerging economies, examining the opportunities and challenges embedded in this transition, and discussing the implications for businesses and consumers alike. Data and Methods. To achieve these objectives, we used a quantitative approach, surveying 872 Thai participants through an online questionnaire using a convenience sampling technique. Additionally, we analyzed the data comparing e-commerce and s-commerce across Southeast Asian countries using the documentary method and content analysis. Results. Consumer spending through e-commerce and s-commerce has a significant positive impact on economic growth in Thailand, surpassing the impact of government spending. Private consumption, a substantial component of Thailand's GDP, stimulates production, investment, and job creation, fostering overall economic advancement. In Southeast Asia, distinct e-commerce trends are evident: Thailand benefits from high internet and smartphone usage, Indonesia from robust social media engagement, and Vietnam from a focus on social commerce and mobile, cross-border e-commerce. These diverse trends underscore the necessity for businesses to tailor their strategies to each country's unique consumer behaviors and preferences. Conclusions. The study confirms the significant impact of electronic consumption through e-commerce and social media on GDP growth. This form of consumption not only drives demand but also creates jobs, enhances efficiency, and opens up opportunities for international trade, fostering sustained economic development. In light of these findings, governments are advised to bolster digital infrastructure and support businesses in their digital transition. Meanwhile, businesses are recommended to adapt to digital models, emphasize consumer engagement, expand globally through online platforms, and integrate sustainable practices. Collectively, these measures are designed to harness the full potential of electronic consumption for sustainable and robust economic growth.

Certain classes of analytic Functions involving multiplier transformations by using q-calculus operators

In this paper we define the classes using Janowski class, multiplier transformations and q-calculus. The results investigated for these classes of functions include the co-efficient estimates, inclusion relations, distortion bounds. Extreme points and many more properties.

Properties of a Special Holomorphic Function Linked with a Generalized Multiplier Transformation

In the present paper, we introduce a special holomorphic function in U={z∈C:|z|<1} which is associated with new generalized multiplier transformations. We investigate several properties of the defined function using the concept of subordination, then highlight a number of cases with interesting results.

Family of Analytic Functions with Negative Coefficients Involving $q-$Analogue of Multiplier Transformation Operator

We introduce a new class of analytic functions with negative coefficients by using the $q-$analogue of multiplier transformation operator. Coefficient inequalities, distortion theorems, closure theorems, and some properties involving the modified Hadamard products, radii of close-to-convexity, starlikeness, and convexity, and integral operators associated with functions belonging to this class are obtained.

Properties of a subclass of analytic functions defined by Riemann-Liouville fractional integral applied to convolution product of multiplier transformation and Ruscheweyh derivative

Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.

Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation

In this paper, the author combines the geometric theory of analytic function regarding differential superordination and subordination with fuzzy theory for the convolution product of Ruscheweyh derivative and multiplier transformation. Interesting fuzzy inequalities are obtained by the author.

Research on the prediction model of agricultural drought hazard considering the time-delayed cumulative effect and system development characteristics

Agricultural drought hazard is a complex time-delayed system affected by multiple hazard factors. The ability to estimate agricultural drought hazard accurately is crucial for guaranteeing food security. A TDMGM(1,m,N) prediction model coupling the time-delayed cumulative driving effect of multi-factor and the development characteristics of multi-system is constructed by introducing the time-delayed driving term and simultaneous formula with the goal of solving the problem of multivariate time-delayed prediction modeling of agricultural drought hazard. The definition form and derivation form of the TDMGM(1,m,N) model are given under the two cases of small and large variations of relevant variables, and the nonlinear solutions of the optimal delay parameters are given by using the fmincon function in Matlab. The solution method for model parameter estimation is also provided. It is proved that GM(1,1), GM(1,N), time-delayed GM(1,N), MGM(1,m) and MGM(1,m,N) are all special forms of TDMGM(1,m,N) model. The effect of multiplier transformation on model parameters, simulation prediction value, and model accuracy is also investigated. Finally, the TDMGM(1,m,N) model is applied to predict agricultural drought hazard in Henan Province. The findings demonstrate that the model can address the prediction problem of multiple system characteristic variables when multiple relevant variables exhibit time-delayed properties with good fitting and prediction accuracy.

Strong Differential Subordination and Superordination Results for Extended q-Analogue of Multiplier Transformation

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided.

Differential Subordination and Superordination Results for q-Analogue of Multiplier Transformation

The results obtained by the authors in the present paper refer to quantum calculus applications regarding the theories of differential subordination and superordination. These results are established by means of an operator defined as the q-analogue of the multiplier transformation. Interesting differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc U, which is defined and investigated here by using this q-operator.

New Subclass of Analytic Functions Associated with Multiplier Transformation

New Subclass of Analytic Functions Associated with Multiplier Transformation

Fuzzy differential subordination and superordination results for $ q $ -analogue of multiplier transformation

<abstract><p>In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the $ q $-analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc $ U $ which is defined and investigated here by using this $ q $-operator.</p></abstract>

Differential Sandwich Theorems for Atangana–Baleanu Fractional Integral Applied to Extended Multiplier Transformation

In this paper we derive subordination and superordination results regarding the Atangana–Baleanu fractional integral applied to multiplier transformation and we give several differential sandwich-type theorems. Then, we apply the Atangana–Baleanu fractional integral to extended multiplier transformation on the class A ζ ∗ of normalized analytic functions and we derive strong differential subordination and strong differential superordination results regarding the extended new operator and we give the corresponding differential sandwich-type theorems from the first part of the paper.

New Subclass of K -Uniformly Univalent Analytic Functions with Negative Coefficients Defined by Multiplier Transformation

In this work, we shall derive a new subclass of univalent analytic functions denoted by H α , β , γ , k , λ , m in the open unit disk D = z ∈ ℂ : z < 1 which is defined by multiplier transformation. Coefficient inequalities, growth and distortion theorem, extreme points, and radius of starlikeness and convexity of functions belonging to the subclass are obtained.

Multivalent harmonic functions Involving multiplier transformation

In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

Application of a Multiplier Transformation to Libera Integral Operator Associated with Generalized Distribution

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function fs(z) is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions fs(z) are established. Further, by applying a previously introduced linear transformation to fs(z) and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform.

Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus.

Applications of the Atangana–Baleanu Fractional Integral Operator

Applications of the Atangana–Baleanu fractional integral were considered in recent studies related to geometric function theory to obtain interesting differential subordinations. Additionally, the multiplier transformation was used in many studies, providing elegant results. In this paper, a new operator is defined by combining those two prolific functions. The newly defined operator is applied for introducing a new subclass of analytic functions, which is investigated concerning certain properties, such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and radii of starlikeness, convexity and close-to-convexity. This class may have symmetric or asymmetric properties. The results could prove interesting due to the new applications of the Atangana–Baleanu fractional integral and of the multiplier transformation. Additionally, the univalence properties of the new subclass of functions could inspire researchers to conduct further investigations related to this newly defined class.

On a Class of Function of Bounded Turning with Negative Coefficients Associated with a Generalized Multiplier Transformation

The study of univalent functions and its applications is an hallmark of geometric function theory. Since univalent functions are analytic and has one-to-one mapping, it has a wide range of applications in the fields of studies where transformations (enlargements and reductions) are done. The functions also have angle and orientation preserving properties among other uses. Many authors have defined and studied various classes of univalent functions using different approaches and tools. In this study however, the authors used a generalized multiplier transformation to define a and investigate a new class of functions T_σ^n (λ). Various properties of the class of functions were investigated. The results extend some known results in literature.

New Applications of Fractional Integral for Introducing Subclasses of Analytic Functions

The fractional integral is prolific in giving rise to interesting outcomes when associated with different operators. For the study presented in this paper, the fractional integral is associated with the convolution product of multiplier transformation and the Ruscheweyh derivative. Using the operator obtained as a result of this association and inspired by previously published results obtained with similarly introduced operators, the class of analytic functions IR(μ,λ,β,γ,α,l,m,n) is defined and investigated concerning various characteristics such as distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to this class.