Some Extensions of Banach’s Contraction Principle in Complete Cone Metric Spaces
نویسندگان
چکیده
The study of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity, for example see 1–5 and it has a wide range of applications in different areas such as nonlinear and adaptive control systems, parameterize estimation problems, fractal image decoding, computing magnetostatic fields in a nonlinear medium, and convergence of recurrent networks, see 6–10 . Recently, Huang and Zhang generalized the concept of a metric space, replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfying different contractive conditions 11 . The study of fixed point theorems in such spaces is followed by some other mathematicians, see 12–15 . The aim of this paper is to generalize some definitions such as c-nonexpansive and c, λ -uniformly locally contractive functions in these spaces and by using these definitions, certain fixed point theorems will be proved. Let E be a real Banach space. A subset P of E is called a cone if and only if the following hold:
منابع مشابه
Fixed Point Theorems for Set-Valued Generalized Contractive Maps in Cone Metric Spaces
Banach’s contraction principle plays an important role in several branches of mathematics. Because of its importance for mathematical theory, it has been extended in many direction. Especially, Nadler [23] gave a generalization of Banach’s contraction principle to the case of set-valued maps in metric spaces. The author [13] obtained a generalization of Nadler’s fixed point theorem. They proved...
متن کاملThe Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces
It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...
متن کاملExtensions of Some Fixed Point Theorems for Weak-Contraction Mappings in Partially Ordered Modular Metric Spaces
The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.
متن کاملThe Banach Type Contraction for Mappings on Algebraic Cone Metric Spaces Associated with An Algebraic Distance and Endowed with a Graph
In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...
متن کاملCommon fixed points of f-weak contractions in cone metric spaces
Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and als...
متن کامل