Generalized $c$-almost periodic type functions in ${\mathbb{R}}^{n}$

Abstract

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Metrical approximations of functions

“…In what follows, we investigate the relationship between the notions of semi-(φ, c j , F, B, P) j∈Nn -periodicity and the semi-(φ, c j , F, B, P) j∈Nn -periodicity of type 1 (2); cf. also [19,Theorem 2.10]: Proposition 2.12. Suppose that condition (C3) holds, φ(0) = 0 and there exists a finite real constant c > 0 such that φ(x + y) ≤ c[φ(x) + φ(y)] for all x, y ≥ 0.…”

“…cf. also [19,Example 2.11] for the multi-dimensional analogue of this example. Now we will prove that f (•) is p-semi-anti-periodic function in variation (1 ≤ p < +∞), i.e., semi-(x, −I, 1, P)-periodic with P being the subspace…”

Multi-dimensional Besicovitch almost periodic type functions and applications

“…The class of multi-dimensional ρ-almost periodic type functions, extending the class of multi-dimensional c-almost periodic type functions when ρ = cI, have recently been investigated by M. Fečkan et al [27]; see also [43]- [44]. The class of Besicovitch-(p, c)-almost periodic functions, where 1 ≤ p < ∞ and c = 1, has not been analyzed in the existing literature so far, even in the one-dimensional setting.…”

STEPANOV $\rho$-ALMOST PERIODIC FUNCTIONS IN GENERAL METRIC

“…The multi-dimensional ρ-almost periodic type functions, the Stepanov multidimensional ρ-almost periodic type functions and the Weyl multi-dimensional ρalmost periodic type functions have recently been examined in [6], [12] and [13].…”