The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integr...Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.展开更多
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
基金the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2016AM03 and ZR2017M A011).
文摘Using an operator ordering method for some commutative superposition operators,we introduce two new multi-variable special polynomials and their generating functions,and present some new operator identities and integral formulas involving the two special polynomials.Instead of calculating compli-cated partial differential,we use the special polynomials and their generating functions to concsely address the normalzation,photoount distributions and Wigner distributions of several quantum states that can be realized physically,the rsults of which provide real convenience for further investigating the properties and applications of these states.
