A Unified Geometric Function Theory Framework for Subordination–Superordination Preserving Transformations via Wright-Type Generalized Hypergeometric Integral Operators in Multivalent Function Classes
Keywords:
Geometric function theory, subordination, superordination, Wright generalized hypergeometric function, multivalent functionsAbstract
This paper develops a unified geometric function theory framework for analyzing subordination–superordination preserving transformations generated by Wright-type generalized hypergeometric integral operators within multivalent analytic function classes. The study integrates classical geometric function theory, fractional and integral operator theory, and modern subordination–superordination techniques to construct a generalized operator-based analytic structure. The proposed framework extends existing linear and integral operator approaches by embedding Wright generalized hypergeometric functions into multivalent function transformations, thereby enabling a broader characterization of inclusion, dominance, and invariance properties.
The theoretical foundation relies on differential subordination principles, integral transform operators, and analytic continuation properties of hypergeometric-type functions. Emphasis is placed on preserving geometric properties such as starlikeness, convexity, and univalence under operator action. The study further establishes sufficient conditions for subordination and superordination preservation using structured inequalities and analytic constraints.
The results demonstrate that Wright-type integral operators preserve key geometric properties under appropriate parameter conditions and provide a unified mechanism for mapping between subclasses of p-valent analytic functions. The framework generalizes earlier results in differential subordination theory and fractional operator analysis, offering a more comprehensive structural understanding of analytic function transformations.
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