Browsing by Author "Sahin Bayram, Nilay"

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    Criteria for statistical convergence with respect to power series methods
    (2021) Sahin Bayram, Nilay; https://orcid.org/0000-0003-3263-8589; GPT-3667-2022
    In the present paper we give some criteria for statistical convergence with respect to power series method. The main tool for providing this result is the inverse Fourier transformation. We will also deal with sequences x that admit a factorization x=yz in which y is strongly convergent and z is statistically convergent with respect to a power series method.
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    Multipliers and I-core for sequences
    (2021) Gulfirat, Mustafa; Sahin Bayram, Nilay; 0000-0003-3263-8589; GPT-3667-2022
    In this paper we mainly deal with I-c((q)) - convergence. In particular we study bounded multipliers of bounded I-c((q) )- convergent sequences. We also give some I-core results and characterize the inclusion K-core {Ax} subset of I-core {x} for bounded sequences x = (x(n)).
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    P-Strong Convergence With Respect To An Orlicz Function
    (2022) Sahin Bayram, Nilay; GPT-3667-2022
    The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently unver and Orhan [19] have introduced the concepts of P-strong and P-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of P-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies o2- condition. We also get an improvement of this result by using the concept of uniform integrability.