denote the open ball of radius a centred on the origin in IR. If the function ~g : Ba → IR d obeys there is a constant G < 1 such that ‖~g(~x)− ~g(~y)‖ ≤ G ‖~x− ~y‖ for all ~x, ~y ∈ Ba (H1) ‖~g(~0)‖ < (1−G)a (H2) then the equation ~x = ~g(~x) has exactly one solution. Discussion of hypothesis (H1): Hypothesis (H1) is responsible for the word “Contraction” in the name of the theorem. Because G <...

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...

Abstract In this article, we introduce two new types of generalized contraction mappings in double controlled metric type spaces: Θ-double mapping and Ćirić-Reich-Rus-type-Θ-double mapping. For each mapping, establish the existence uniqueness fixed point theorems on complete space provide examples. We present an application our results demonstrate how generalize several existing literature.

In this work, we give a partial positive answer to the question concerning set-valued quasicontraction proposed by Amini-Harandi (Appl. Math. Lett. 24:1791-1794 2011). By useful lemma, prove fixed point theorem for quasi-contraction, which extends range of contraction constant in result from [0, 1/2) 1/3? 3). Also, new simple proof quasi-contraction type Haghi et al. 25:843-846 2012). Finally, ...

Darbo fixed point theorem is a powerful tool which used in many fields mathematics. Because of this feature, generalizations and its relations with other subjects have been investigated. Here we introduce generalization an F - contraction type mapping define new by using both function lasses uniformly convergent sequences functions examine some properties. Afterward, show that the contraction, ...

In this paper, we prove a fixed point theorem for the sum of a nonlinear contraction mapping and compact operator. The fixed point theorem obtained here resembles that of Krasnoselskii in which the mapping function is a combination of contraction and compact operators. It also takes the form of Schaefer’s fixed point theorem of continuation type. Criteria on periodicity and control in integral ...

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas is used to investigate the existence and uniqueness of solutions to first-order boundary value problems for impulsive functional differential equations with infinite delay. An example to illustrate the results is included.

In this paper, we consider a class of nonlinear fuzzy integral equations of fractional order. The existence and uniqueness of solutions are established by the generalized Schauder theorem and contraction mapping principle.

In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fix...