I-limit superior and limit inferior

By Kamil Demirci. 2001

147 citations recorded by the source corpus.

In this paper we extend concepts of statistical limit superior and inferior (as introduced by Fridy and Orhan) to I−limit superior and inferior and give some I−analogue of properties of statis- tical limit superior and inferior for a sequence of real numbers. Also we extend the concept of the statistical core to I−core for a complex num- ber sequence and get necessary conditions for a summability matrix A to yield I−core {Ax }⊆I −core {x} whenever x is a bounded complex number sequence.

View Paper: https://www.semanticscholar.org/paper/162945a26ee0ba55f37ca0e50920e68638842d00

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Citations in the corpus

On I-Acceleration Convergence of Sequences of Fuzzy Real Numbers (2012, methodology): “Anal., 17(4):549–557, 2012. with summability theory by Demrici [10], Tripathy and Hazarika [20, 21, 22, 23] and many others.”
ROUGH IDEAL CONVERGENCE (2013, background): “(A sequence {xi}i∈N is said to be I-bounded if there exists a positive real number G such that the set A = {i ∈ N : ‖xi‖ ≥ G} ∈ I)[7].”
I-Monotonic and I-Convergent Sequences (2011, background): “Later on it was studied by Salat, Tripathy and Ziman ([8], [9]), Demirci [1], Tripathy and Hazarika ([16], [17], [18]), Tripathy and Mahanta [20] and others.”
Rough I-Convergence (2014, background): “[3] K. Demirci, I-limit superior and limit inferior, Math.”
Abstract Korovkin-type theorems in modular spaces and applications (2013, background): “Note that the limit, limit superior and limit inferior with respect to Fcofin coincide with the usual ones [15].”
Paranorm I-convergent sequence spaces (2009, background): “Later on it was studied by Š a l á t , T r i p a t h y and Z i m a n [8], [9], D e m i r c i [1] and many others.”