(5.1) The contraction mapping principle Let 0 ≤ r < 1. Let (X, d) be a nonempty metric space and f : X → X be a function that is a strict contraction, that is, for all x, y ∈ X, d(f(x), f(y)) ≤ rd(x, y). Then f has a unique fixed point. proof Existence of a fixed point: Let x0 ∈ X, and define the sequence (xn)n by: for all n ∈ N, xn+1 = f(xn). Then (xn)n is a Cauchy sequence: first, we have by ...

Importance of contraction for belief change notwithstanding, literature on iterated belief change has by and large centered around the issue of iterated belief revision, ignoring the problem of iterated belief contraction. In this paper we examine iterated belief contraction in a principled way, starting with Qualified Insertion, a proposal by Hans Rott. We show that a judicious combination of ...

This article deals with a 2 ? reaction-diffusion-taxis model consisting of Michaelis-Menten functional response predator-prey system. The critical section this is that temporal-spatial evolution the predators? velocity depends largely on gradient prey. But beyond that, system also inscribes prey-taxis mechanism an immediate movement predator u in to change prey v (which leads collection u). By ...

The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively recent past. Suitable fixed point theorem to be selected study boundary value due properties exhibited difference operators. This article aims at investigating stability results sense Hyers and Ulam with application Mittag–Leffler function hybrid or...

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.

This paper establishes a study on some important latest innovations in the uniqueness of solution for Caputo fractional Volterra-Fredholm integro-differential equations. To apply this, the study uses Banach contraction  principle and Bihari's inequality.  A wider applicability of these techniques are based on their reliability and reduction in the size of the mathematical work.

Celebrated Banach’s contraction mapping principle is one of the cornerstones in the development of nonlinear analysis. Fixed point theorems have applications not only in the various branches of mathematics but also in economics, chemistry, biology, computer science, engineering, and others. In particular, such theorems are used to demonstrate the existence and uniqueness of a solution of differ...

*Correspondence: [email protected] 1School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410075, P.R. China 2School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, P.R. China Full list of author information is available at the end of the article Abstract By using Schauder’s fixed poin...

Fixed point and coincidence results are presented for multivalued generalized n -weak contractive mappings on complete metric spaces, where N: [0, +4) ÷ [0, +4) is a lower semicontinous function with N (0) = 0 and N (t) > 0 for all t > 0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969) and DaTer and Kaneko (1995). Branciari (2002) gave a...

The problem on global exponential stability of antiperiodic solution is investigated for a class of impulsive discrete-time neural networks with time-varying discrete delays and distributed delays. By constructing an appropriate Lyapunov-Krasovskii functional, and using the contraction mapping principle and the matrix inequality techniques, a new delay-dependent criterion for checking the exist...