Some results on (δ-pre, s)-continuous functions

One of the important and basic topics in general topology and several branches of mathematics which have been researched by many authors is the continuity of functions. In this paper, we study (δ-pre, s)-continuous functions as a new weaker form of continuity. In 1996, Dontchev [3] introduced contra-continuous functions, and Jafari and Noiri [10] introduced contra-precontinuous functions (in 2002). Ekici [8] studied the notion of almost contra-precontinuous functions. Recently, Ekici [7] introduced and studied the notion of (δ-pre, s)-continuous functions as a new weaker form of almost contraprecontinuous functions. The aim of this paper is to study some properties of (δ-pre, s)-continuous functions and modification of the results due to Ekici [7]. Basic characterizations concerning (δ-pre, s)-continuous functions are investigated and some results are obtained. Moreover, we obtain some properties in general cases concerning composition of functions under specific conditions, where the composition would yield a (δ-pre, s)-continuous function. Finally, if given a composition of functions, which are (δ-pre, s)-continuous, we obtain the first function in the composition, which will be (δ-pre, s)continuous.