Abstract: In this letter, we explore exact solutions for the
Horava-Lifshitz gravity. We use of an extension of this theory with
first order dynamical lapse function. The equations of motion have
been derived in a fully consistent scenario. We assume that there
are some spherically symmetric families of exact solutions of this
extended theory of gravity. We obtain exact solutions and investigate
the singularity structures of these solutions. Specially, an exact
solution with the regular horizon is found.
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: The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.
Abstract: The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are 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 IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: The purpose of this paper is to present the fuzzy contraction
properties of the Hutchinson-Barnsley operator on the fuzzy
hyperspace with respect to the Hausdorff fuzzy metrics. Also we
discuss about the relationships between the Hausdorff fuzzy metrics
on the fuzzy hyperspaces. Our theorems generalize and extend some
recent results related with Hutchinson-Barnsley operator in the metric
spaces.
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.
Abstract: We study a long-range percolation model in the hierarchical
lattice ΩN of order N where probability of connection between
two nodes separated by distance k is of the form min{αβ−k, 1},
α ≥ 0 and β > 0. The parameter α is the percolation parameter,
while β describes the long-range nature of the model. The ΩN is
an example of so called ultrametric space, which has remarkable
qualitative difference between Euclidean-type lattices. In this paper,
we characterize the sizes of large clusters for this model along the
line of some prior work. The proof involves a stationary embedding
of ΩN into Z. The phase diagram of this long-range percolation is
well understood.
Abstract: The precise form of tensorial transformations acting on a given collection of infinite matrices into another ; for such classical ideas connected with the summability field of double gai sequence spaces. In this paper the results are impose conditions on the tensor g so that it becomes a tensorial transformations from the metric space χ2 to the metric space C