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In this paper we introduce the concept of quadratic operator perspective fora continuous function {\Phi} defined on the positive semi-axis of real numbers.This generalize the quadratic weighted operator geometric mean and thequadratic relative operator entropy. Some inequalities for this perspective ofconvex functions are established. Applications for quadratic weighted operatorgeometric mean and quadratic relative operator entropy are also provided.

Inequalities for Quadratic Operator Perspective of Convex Functions and Bounded Linear Operators in Hilbert Spaces