Symmetrically continuous functions

Abstract

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Remarks on Uniformly Symmetrically Continuous Functions

“…Let n ≥ N. By ( 12), (13), and the construction of A, we obtain that x n and y n lie in the interval [a 4k−3 , a 4k−2 ] ∪ [a 4k−1 , a 4k ] for some k ∈ N. Suppose that x n and y n lie in different intervals, say x n ∈ [a 4k−3 , a 4k−2 ] and y n ∈ [a 4k−1 , a 4k ]. Then…”

“…Like continuous functions, symmetrically continuous functions have been studied thoroughly by many authors, see for example in [2], [3], [4], [5], [8], [9], [10], [11], [12], [13], [14], and [15]. In particular, Marcus [7] writes an article on various types of symmetry on the real line such as symmetric sets, asymmetric sets, antisymmetric sets, symmetric functions, symmetric continuities, and symmetric derivatives.…”

“…For some results about symmetric continuity on subsets of the real line, we refer the reader to [13] and [14]. An answer to Problem 1 given by Kostyrko [6] can be stated in our language as follows: The purpose of this article is to investigate further the properties of uniformly symmetrically continuous functions defined on a nonempty subset of R and compare them with those of continuous functions, uniformly continuous functions and symmetrically continuous functions defined on the same domain.…”

Weakly Symmetrically Continuous Functions

“…Then a study of sequences of weakly symmetrically continuous functions will be given in Section 4. We refer the reader to [1,2,3,4,5,6,8,9,13,14,15,16] for other results concerning symmetric continuity of functions. We end this section by giving some results that will be used later.…”