Applications of fractional difference operators for new version of Brudno-Mazur Orlicz bounded consistency theorem

Kuldip Raj; Anu Choudhary; Mohammad Mursaleen

doi:10.5269/bspm.62670

Kuldip Raj Shri Mata Vaishno Devi University https://orcid.org/0000-0002-2611-3391
Anu Choudhary Shri Mata Vaishno Devi University
Mohammad Mursaleen China Medical University https://orcid.org/0000-0003-4128-0427

Résumé

In this paper, we intend to prove that the modulus $\mathcal{A}-$lacunary statistical convergence of fractional difference double sequences and modulus lacunary fractional matrix of four-dimensions taken over the space of modulus $\mathcal{A}-$lacunary fractional difference uniformly integrable real sequences are equivalent. We represent another version of the Brudno-Mazur Orlicz bounded consistency theorem by using modulus function, lacunary sequence, and fractional difference operator. We show that the four-dimensional $RH-$ regular matrices $\mathcal{A}$ and $\mathcal{B}$ are modulus lacunary fractional difference consistent over the multipliers space of modulus fractional difference $\mathcal{A}-$summable sequences and an algebra $Z.$

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Bibliographies de l'auteur

Kuldip Raj, Shri Mata Vaishno Devi University

Department of Mathematics

Anu Choudhary, Shri Mata Vaishno Devi University

Department of Mathematics

Mohammad Mursaleen, China Medical University

Department of Mathematics

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