Geodesic
Metrical Bochner criterion and metrical Stepanov almost periodicity
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 90-100

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We analyze the metrical Bochner criterion and a new class of multi-dimensional metrically Stepanov almost periodic type functions. We clarify the main structural properties for the introduced classes of functions, including the Bochner criterion, and provide certain applications to Doss-$p$-almost periodic functions. We also study the extensions of almost periodic sequences and briefly explain how we can apply the established theoretical results to the abstract Volterra integro-differential equations.
Keywords: metrically Stepanov $\rho$-almost periodic type function, convolution invariance, abstract Volterra integro-differential equation. 
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     title = {Metrical {Bochner} criterion and metrical {Stepanov} almost periodicity},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {90--100},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a6/}
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M. Kostić; V. E. Fedorov; H. C. Koyuncuoğlu. Metrical Bochner criterion and metrical Stepanov almost periodicity. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 90-100. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a6/