Abstract: In this paper, we introduce R Iterated Function System
and employ the Hutchinson Barnsley theory (HB) to construct a
fractal set as its unique fixed point by using Reich contractions in a
complete b metric space. We discuss about well posedness of fixed
point problem for b metric space.
Abstract: The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.
Abstract: Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.
Abstract: This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic
fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the
standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze
some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic
fuzzy metrics.
Abstract: The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.