Extensions of different type parameterized inequalities for generalized (m,h) $(m,h)$-preinvex mappings via k-fractional integrals

Abstract

Abstract The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h) $(m,h)$-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some interesting results are also obtained.

Keywords

• Hermite–Hadamard’s inequality
• Simpson’s inequality
• Generalized ( m , h ) $(m,h)$ -preinvex functions
• k-fractional integrals