Abstract
The notion of a lacunary statistical d 2 -quasi-Cauchyness of sequence of real numbers is introduce and investigated. In this work, we present interesting theorems related to lacunary statistically d 2 -ward continuity. A function f, whose domain is included in R, and whose range included in R is called lacunary statistical d 2 ward continuous if it preserves lacunary statistical d 2 quasi-Cauchy sequences, i.e. (f(x k )) is a lacunary statistically d 2 quasi-Cauchy sequence whenever (x k ) is a lacunary statistically d 2 quasi-Cauchy sequence, where a sequence (x k ) is called lacunary statistically d 2 quasi-Cauchy if ( D 2 x k ) is a lacunary statistically quasi-Cauchy sequence. We find out that the set of lacunary statistical d 2 ward continuous functions is closed as a subset of the set of continuous functions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
