On the distribution of αp modulo one in the intersection of two Piatetski-Shapiro sets

Let (sic)t(sic) denote the integer part of t is an element of R and parallel to x parallel to the distance from x to the nearest integer. Suppose that 1/2<gamma 2<gamma 1<1 are two fixed constants. In this paper, it is proved that, whenever alpha is an irrational number and beta is any real number, there exist infinitely many prime numbers p in the intersection of two Piatetski-Shapiro sets, i.e., p=(sic)n(1)(1/gamma 1)(sic)=(sic)n(2)(1/gamma 2)(sic), such that parallel to alpha p+beta parallel to<p-(12(gamma 1+gamma 2)-23)/(38)+epsilon, provided that 23/12<gamma 1+gamma 2<2. This result constitutes an generalization upon the previous result of Dimitrov (Indian J Pure Appl Math 54(3):858-867, 2023).