LpL_p-Bounds for the \v{C}eby\v{s}ev functional

In this paper several new bounds for the \v{C}eby\v{s}ev functional involving $L_p$-norm are presented.Comment: This work contains inaccurate results. Some results do not hold. There are scientific flaw

On Pompeiu-Cebysev type inequalities for positive linear maps of selfadjoint operators in inner product spaces

In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1708.0644