ANALYTICAL PROPERTIES ON MULTIPLICATIVELY MψA-p-FUNCTIONS AND RELATED MULTIPLICATIVE ψ-HILFER FRACTIONAL TRAPEZOID-TYPE INEQUALITIES

The primary objective of this study is to explore the properties and inequalities associated with multiplicatively [Formula: see text]-[Formula: see text]-functions. We commence our investigation by introducing the concept of multiplicatively [Formula: see text]-[Formula: see text]-functions, followed by an analysis of their characteristics. Subsequently, we introduce the multiplicative [Formula: see text]-Hilfer fractional integrals and formulate an identity involving these operators. Based on this identity, we establish some trapezoid-type inequalities that are applicable to multiplicatively [Formula: see text]-[Formula: see text]-functions. Additionally, we provide several illustrative examples to validate our theoretical findings. Finally, we discuss the applications of the obtained outcomes, linking them to numerical quadrature formulas, and special mean value estimates.