Search Results (228)

In this paper, we introduce a new class of bi-univalent functions defined by a third-order logarithmic-type differential operator. By using the subordination principle and Carathéodory functions, we investigate the coefficient estimates for the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Furthermore, we derive the Fekete–Szegö inequality and obtain bounds for the second Hankel determinant $H_2\left(2\right)$ associated with this class. Several consequences of the main results are also discussed. Full article

In this paper, certain subclasses of meromorphic harmonic functions which are formulated using a q-differential operator are meticulously analyzed. Initially, two new subclasses $W_H^q(k;E,F)$ and $W_{\eta }^q(k;E,F)$ associated with the Janowski function with relevance to the idea of weak subordination are defined. These classes are further studied through their various analytical and geometric properties. Some of these explored properties include the necessary and sufficient coefficient condition, the radii of starlikeness, characterizations of extreme points, distortion estimation, closeness under convolution, and convex combination features. Additionally, the asymptotic behavior of the coefficients is also examined, and to express the findings, the Big-O, little-o, and asymptotic equivalency notations are used. These findings significantly represent the interaction between the growth, dominant terms, and limiting behavior of functions within these subclasses. Full article

This study examines how two types of workplace fun—sociality-oriented fun and assistant-oriented fun—relate to different forms of employees’ innovative behavior through positive affect and job satisfaction, drawing on the Affective Events Theory and the motivational dimensional model of affect. Data were collected from 17 supervisors and 116 employees in a Chinese state-owned electric power company using a supervisor-subordinate dyadic survey procedure. Mplus 8.3 was used to test the hypothesized model. The results show that sociality-oriented fun is positively associated with affect-driven innovative behavior through high-motivated positive affect, whereas assistant-oriented fun is positively associated with judgment-driven innovative behavior through the serial mediating role of low-motivated positive affect and job satisfaction. These findings provide a more differentiated understanding of how workplace fun may shape employee innovation and offer practical implications for designing fun activities that align with different innovation goals. Full article

The theory of analytic functions remains a fundamental area of geometric function theory, with particular emphasis on coefficient problems, differential subordinations, and determinant estimates. Motivated by recent developments in fractional calculus and quantum calculus, this paper introduces two new subclasses of normalized analytic functions by employing the subordination principle in combination with the q-derivative operator and the q-Sălăgeăn differential operator within the framework of quantum calculus. The inclusion of fractional and q-calculus techniques provides a more flexible and generalized approach to classical problems in complex analysis, enabling deeper structural insights into analytic function classes. Using the subordination framework, we derive coefficient relations for the proposed subclasses. Furthermore, we establish sharp upper bounds for the Fekete–Szegö functional $|a_3-\delta a_2^2|$ and for the second Hankel determinant $H_{2,2}\left(f\right)=a_2{a}_4-a_3^2$. The obtained results extend and unify several known works in the literature and demonstrate how the interaction between fractional calculus, quantum operators, and subordination theory can be effectively used in geometric function theory. Finally, the presented approach opens the door for further investigations involving higher-order Hankel determinants, other subclasses of analytic functions, and potential extensions involving special functions and fractional operators. Full article

The Arco Verde Complex, exposed in the Serra do Inajá region of the Rio Maria Domain (Carajás Province, Amazonian Craton), represents one of the oldest TTG granitoid association of the province (3.00–2.92 Ga). While TTG magmatism is well constrained in the northern domain, its southern sector lacks precise geochronological data. This study integrates petrographic, geochemical, U–Pb zircon geochronology, and Nd–Hf isotopes to constrain the age, source, and crustal significance of these granitoids. Uranium–Pb zircon dating of two granodiorites yielded ages of 2979 ± 8 and 2979 ± 11 Ma, extending the 2.98 Ga TTG magmatic episode to the southern sector of the Rio Maria Domain. Geochemical data indicate dominant tonalites formed by partial melting of a similar mafic source at different crustal depths, whereas subordinate granodioritic and monzogranitic rocks show transitional TTG affinities. These features indicate coeval mafic and felsic crust rapidly reworked after formation. Hf and Nd model ages of 3.0–3.2 Ga, with positive ε_Hf–Nd at 2.98 Ga, reinforce the Early Mesoarchean as the main crustal growth period in the province. In addition, we propose that the differentiation of the depleted mantle (DM) beneath the Carajás Province may have initiated around 3.8 Ga. Full article

Art therapy assessment benefits from analytical clarity while preserving non-directive, process-sensitive practice. Although the Expressive Therapies Continuum (ETC) is widely used to conceptualize sensory, affective, cognitive, and symbolic processes in art-making, ETC-informed assessment often relies on implicit clinical reasoning, limiting transparency and interdisciplinary communication. This article presents the developmental stage of a protocol-based Expressive Therapies Continuum Assessment Profile (ETC-AP) developed at Rīga Stradiņš University. The ETC-AP differentiates activation and inhibition patterns around integration midpoints and organizes observation in a defined five-step interpretive sequence without positioning the method as a psychometrically validated test. It combines (i) a uniform three-task, non-directive administration with a brief post-task inquiry; (ii) criteria-guided coding of observable features across three artworks and process notes; and (iii) 0–100 descriptive profile indicators to support within-case pattern description and professional dialogue. An illustrative case vignette shows how the ETC-AP can generate trauma-informed, regulation-oriented hypotheses about channel accessibility and cautious regulation-oriented sequencing, while remaining subordinate to clinical judgment and context. Key boundaries include incomplete operational coverage in some inhibition ranges, limits of static documentation for process-dependent markers, and the need for structured training materials and programmatic studies of reliability, feasibility, and sensitivity to change. Full article

This article focuses on the notions of third-order fuzzy differential subordination and superordination associated with the generalized Mittag-Leffler operator. Methods emphasizing the key concept of admissible functions are implemented to investigate several third-order fuzzy differential subordination and superordination results. Sandwich-type outcomes are established based on the adopted methodology, linking the dual fuzzy theoretical frameworks. In addition, the applications of fuzzy differential subordination are discussed in the context of decision making problems. The proposed approach provides the mathematical mechanism that ensures the stability and preservation of the decision under changes in criteria and preference evaluations, highlighting the importance of the developed theory. Full article

This study investigates third-order differential subordination and its influence on classes of analytic functions associated with the Lommel function of the first kind. By employing a newly defined operator ${\mathbb{L}}_{\mathrm{w}}^{\mathrm{j}}f\left(z\right)$, we identify and characterize the admissible function classes that satisfy the corresponding third-order differential subordinations. These admissibility conditions enable the derivation of several key results, including a sandwich-type theorem obtained as a direct consequence of the established framework. The findings contribute to a broader understanding of analytic functions governed by higher-order differential constraints and highlight the significant role played by the Lommel function in shaping these geometric properties. Full article

q-calculus and fractional calculus combined with geometric function theory lead to remarkable results. The fractional integral introduced by Riemann–Liouville applied to the q-multiplier transformation is used in this research to study the two dual theories of fuzzy differential subordination and fuzzy differential superordination and to develop specific fuzzy results. In the theorems examining fuzzy differential subordinations and fuzzy differential superordinations, fuzzy best dominants and fuzzy best subordinants are also provided. In addition, the demonstrated outcomes reveal corollaries by taking specific functions with established geometric features into consideration as the fuzzy best subordinant and fuzzy best dominant. The work concludes with a fuzzy differential sandwich theorem and related corollaries that combine the findings of this research on fuzzy differential subordinations and superordinations. Full article

In this paper, we introduce a new logarithmic integral operator that unifies differentiation and fractional integration within the complex domain. The present work addresses this gap by applying the proposed operator to analytic functions represented by alternating power series. The method demonstrates that the coefficients can be reorganized in a controlled manner without affecting convergence or analytic behavior. Using this framework, we derive third-order differential subordination and superordination results, which naturally lead to corresponding sandwich-type results. The findings confirm that the introduced operator offers an effective analytical tool for studying distortion, growth, and mapping properties of analytic functions, with promising potential for future applications in fluid mechanics. Full article

The concept of fuzzy differential subordination was introduced in 2011 as a natural generalization of classical differential subordination, reflecting the contemporary trend of incorporating fuzzy set theory into well-established mathematical frameworks. This work aims to explore multiple fuzzy differential subordinations (FDS) and fuzzy differential superordinations (FDSs) associated with the linear multiplier fractional q-differintegral operator. Utilizing the linear multiplier fractional q-differintegral operator, we introduce a novel fuzzy subclass of analytic functions, denoted by $\mathcal{S}{\mathfrak{D}}_{\mathfrak{F}}^{\sigma ,\mathfrak{m}}(q,\lambda ,\gamma )$. Using the concept of FDS and FDSs, we identify important characteristics and analytical aspects of the class $\mathcal{S}{\mathfrak{D}}_{\mathfrak{F}}^{\sigma ,\mathfrak{m}}(q,\lambda ,\gamma )$. Furthermore, we derive a collection of FDS and FDSs results specifically related to the linear multiplier fractional q-differintegral operator. Full article

While over a hundred articles discuss second-order differential inequalities and subordinations in the complex plane, very few address the relatively unexplored classes of third-order fuzzy differential subordination and superordination. This paper builds upon the recently proposed concepts of third-order fuzzy differential subordination and superordination, which are developed using a linear operator and a meromorphic function. By applying techniques based on the fundamental notion of admissible functions, we begin by defining the appropriate class of such functions necessary for deriving new results in third-order fuzzy differential subordination. The study reveals the establishment of sandwich-type theorems, linking these new findings with established methods in third-order fuzzy differentiation and superordination theory. Full article

The use of integral and differential operators in geometric function theory has continued to gain interest among researchers in the field of study in recent times. This is due to the wide range of its applications in science, technology and engineering. In this work, therefore, the authors defined and investigated a new subclass of analytic functions in the open unit disk using the $\mathfrak{q}$-Srivastava–Attiya convolution operator and the Jackson’s $\mathfrak{q}$-derivative, by means of the subordination. The authors used two well-known lemmas to determine a sharp upper-bound for the Fekete–Szeg$\ddot{o}$ functional in two different cases. In particular, the authors introduced a new generalized subclass of complex order univalent functions denoted by ${\mathcal{L}}_{\mathfrak{q},\mathfrak{b},\mathfrak{h}}^{\mathfrak{s}}\left(\tau ,,,\Phi \right)$ and derived the coefficient estimates $a_{\iota }(\iota =2,3)$ of the Taylor–Maclaurin series in this class, as well as the Fekete–Szeg$\ddot{o}$ inequality $\left|a_3,-,\aleph ,a_2^2\right|$ for functions in this class. The work generalizes many known results in the literature. Full article

Artificial intelligence is increasingly embedded in service interactions, requiring users to form rapid social judgments about AI communicators based on limited linguistic and contextual cues. This research examines how AI communication tone shapes behavioral intentions through social cognitive processes of role construal and agency attribution. Drawing on politeness theory, formality research, and social cognition perspectives, two scenario-based experiments test whether formal versus casual tone influences responses via attitudes toward the tone and the AI, and how these effects depend on perceptions of AI as a servant-like social actor. Study 1 shows that tone effects are moderated by servant perception and that economic framing, specifically paid versus free access, functions as an antecedent of hierarchical role construal. Study 2 replicates these effects and demonstrates that interaction structure, one-way versus two-way communication, similarly shapes servant perception by signaling differential autonomy. Across both studies, formal tone is more effective when AI is construed as subordinate, whereas casual tone is less effective under hierarchical role frames. By identifying servant perception as a central social cognitive mechanism, this research advances understanding of human judgment and decision making in technology-mediated interactions and offers implications for AI communication design aligned with role expectations. Because both studies rely on U.S. consumers, the findings should be interpreted within cultural contexts characterized by relatively low power distance, where role expectations and hierarchy norms may differ from other cultural settings. Full article