Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two s...

Let (Ω,Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X , whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X . We prove that a multivalued nonexpansive non-self-random operator T :Ω×C → KC(X), 1-χ-contractive mapping, satisfying an inwa...

In this article, we study general backward stochastic Volterra integral equations (BSVIEs). Combining the contractive-mapping principle, stepby-step iteration method and mathematical induction, we establish the existence and uniqueness theorem of M-solution for the BSVIEs. This theorem could be applied directly to many models, for example, using the result to a kind of financial models provides...

Branciari [1] obtained a fixed point result for a single mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality. The second author [3] proved two fixed point theorems involving more general contractive conditions. In this paper, we establish a general principle, which makes it possible to prove many fixed point theorems for a pair of maps of integral ty...

Transseries in the sense of Écalle are constructed using a topological approach. A general contractive mapping principle is formulated and proved, showing the closure of transseries under a wide class of operations. In the second part we give an overview of results and methods reconstruction of actual functions and solutions of equations from transseries by generalized Borel summation with in o...

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small, ac...

2 Department of Applied Mathematics, Chhatrapati Shivaji Institute of Technology, Durg (C.G.), (India) ABSTRACT Image compression is a process of reducing or eliminating all redundant or irrelevant data. The new compression technique called Fractal image compression. This scheme works by partitioning an image into blocks and using contractive mapping to map each range blocks to its matched doma...

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems t...