Akademik Veri Yönetim Sistemi
Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded, Scopus)
Integral inequalities play a crucial role in various areas of numerical analysis, particularly n the development of numerical integration formulas and numerical methods for differential equations. In the context of numerical methods for differential equations, these inequalities can be beneficial in approximating integrals during finite volume schemes over control volumes. This study introduces new integral and derivative operators in q-calculus, which serve as generalizations of existing operators. The fundamental properties and connections of these new operators with the existing ones are discussed in detail. To demonstrate the significance and validity of these new concepts, several novel integral inequalities for convex functions are derived. These inequalities can be helpful in finding error bounds for numerical integration formulas, thus enhancing the accuracy and reliability of numerical analysis techniques. The findings of this research contribute to the ongoing development of q-calculus and its applications in the field of numerical analysis, particularly in the areas of numerical integration and numerical methods for differential equations.