Fejér-Type Inequalities via Generalized Superquadraticity with Application to Cumulative Fatigue Damage
Keywords:
Convex function, s-superquadratic function, Fej\'{e}r integral inequalities, Fatigue mechanics, Cumulative fatigue damage.Abstract
This paper introduces a new class of superquadratic functions, termed s-superquadratic functions. Based on this new definition, two fundamental lemmas are established, forming the basis for the derivation of several refined Fejér-type integral inequalities. Furthermore, the theoretical findings are applied to fatigue mechanics, where the derived inequalities furnish rigorous lower and upper bounds for cumulative fatigue damage under cyclic loading. The proposed estimates incorporate the nonlinear evolution of fatigue damage through the s-superquadratic framework, providing guaranteed bounds for the accumulated fatigue damage based on weighted loading distributions and cycle-dependent damage densities.
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Copyright (c) 2026 Dawood Khan, Ali Ahmed, Aliya, Muhammad Fahad Riaz, Abdul Wahab (Author)
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