73 research outputs found
Ideal-quasi-Cauchy sequences
An ideal is a family of subsets of positive integers which
is closed under taking finite unions and subsets of its elements. A sequence
of real numbers is said to be -convergent to a real number , if
for each \; the set belongs
to . We introduce -ward compactness of a subset of , the set
of real numbers, and -ward continuity of a real function in the senses that
a subset of is -ward compact if any sequence of
points in has an -quasi-Cauchy subsequence, and a real function is
-ward continuous if it preserves -quasi-Cauchy sequences where a sequence
is called to be -quasi-Cauchy when is
-convergent to 0. We obtain results related to -ward continuity, -ward
compactness, ward continuity, ward compactness, ordinary compactness, ordinary
continuity, -ward continuity, and slowly oscillating continuity.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1005.494
Generalized statistical convergence in 2-normed spaces
In this paper we introduce the concept of λ-statistical convergence in 2-normed spaces. Some inclusion relations between the sets of statistically convergent, λ-statistically convergent and statistically λ-convergent sequences in 2-normed spaces are established, where λ = (λm) is a non-decreasing sequence of positive numbers tending to infinity such that λm+1 ≤ λm + 1, λ1 = 1
COMMON FIXED POINT THEOREMS IN COMPLETE PARTIAL METRIC SPACE
The objective of this article is to obtain coincidence points and common fixed point theorem in complete partial metric space. We provide some examples to support the usability of our results
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