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Cover of the book: Elements of q-calculus

Elements of q-calculus

by Vasile-Aurel Căuș

Summary

Geometric function theory investigates how analytic functions (and others) map the unit disk. In parallel, q calculus has emerged as a powerful analytical framework due to its role in quantum theory, orthogonal polynomials, hypergeometric functions, and discrete models in mathematical physics. Unlike classical calculus, which relies on limits and infinitesimal variations, q calculus introduces a discrete deformation parameter that interpolates between difference type and differential structures. In this book, several subclasses of analytic and meromorphic functions defined by q difference, symmetric q difference, and generalized q differential operators are introduced, analyzed, and unified. These subclasses generalize fundamental families such as starlike, convex, close to convex, and Janowski type functions.


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