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A matched space for time scales and applications to the study on functions

’ insightful comments to improve this manuscript. This work was done while Chao Wang was a visiting scholar at Texas A&M University-Kingsville. This work is supported by Youth Fund of NSFC (No. 11601470), Tian

Compactness criteria and new impulsive functional dynamic equations on time scales

In this paper, we introduce the concept of Δ-sub-derivative on time scales to define ε-equivalent impulsive functional dynamic equations on almost periodic time scales. To obtain the existence of solutions for this type of dynamic equation, we establish some new theorems to characterize the compact sets in regulated function space on noncompact intervals of time scales. Also, by...

Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations

In this paper, we use the analysis of relatively dense sets to point out some deficiencies and inaccuracies in the definition of uniformly almost periodic functions which has been proposed in recent works, and we correct it. Some new generalizations of invariance under translation time scales and almost periodic functions are established. Our study will ensure that now we can...

Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy

Chao Wang Ravi P Agarwal In this work, we address the periodic coverage phenomenon on arbitrary unbounded time scales and initiate a new idea, namely, we introduce the concept of changing-periodic time

Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive ∇-dynamic equations on time scales

In the present paper, by introducing the concept of equipotentially almost automorphic sequence, the concept of weighted piecewise pseudo almost automorphic functions on time scales is proposed. Some first results about their basic properties are obtained and some composition theorems are established. Then we apply these to investigate the existence of weighted piecewise pseudo...

Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales

Yongkun Li 0 Chao Wang 0 0 cn Department of Mathematics, Yunnan University Kunming , Yunnan 650091, People's Republic of China In this paper, we first introduce a concept of the mean-value of

Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales

Yongkun Li 0 Chao Wang 0 0 cn Department of Mathematics, Yunnan University Kunming , Yunnan 650091 , People's Republic of China In this paper, we first introduce a concept of the mean-value of