Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.
New Hadamard-type integral inequalities via a general form of fractional integral operators
Abstract The main motivation in this article is to prove a new and general integral identity and to obtain new integral inequalities of various Hadamard types with the help of this identity. Some basic inequalities such as Holder, Young, power-mean and Jensen inequality have been used to obtain inequalities, and it has been determined that the main findings are generalizations and repetitions of many results that exist in the literature. Another impressive aspect of the study is that a new version of the Atangana–Baleanu integral operator is used, which is a very useful integral operator. We have given some simulations to demonsrate the consistency and harmony of this interesting operator for different values of the parameters.
Tradeoffs and limitations in statistically based image reconstruction problems.
TRADEOFFS AND LIMITATIONS IN STATISTICALLY BASED IMAGE RECONSTRUCTION PROBLEMS