Search results for "Common fixed point"
showing 10 items of 66 documents
Common fixed points of generalized contractions on partial metric spaces and an application
2011
Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces
2012
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. In this paper we prove an analogous fixed point result for a self-mapping on a partial metric space or on a partially ordered metric space. Our results on partially ordered metric spaces generalize and extend some recent results of Ran and Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004…
Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dyna…
2014
In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized phi-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.
A result of Suzuki type in partial G-metric spaces
2014
Abstract Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial …
Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations
2013
In this paper, we prove a new common fixed point theorem for four self mappings by using the notions of compatibility and subsequential continuity (alternate subcompatibility and reciprocal continuity) in metric spaces satisfying a general contractive condition of integral type. We give some examples to support the useability of our main result. Also, we obtain some fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. We conclude the paper with an application of our main result to solvability of systems of functional equations.
Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces
2011
We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.
Common fixed point theorems for mappings satisfying common property (E.A.) in symmetric spaces
2011
In this paper, common fixed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.). In the process, a host of previously known results are improved and generalized. We also derive results on common fixed point in probabilistic symmetric spaces.
Common Fixed Point Theorems for Weakly Compatible Maps Satisfying a General Contractive Condition
2008
We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.
On Branciari’s theorem for weakly compatible mappings
2010
AbstractIn a recent paper B. Samet and H. Yazidi [B. Samet, H. Yazidi, An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Ital. J. Pure Appl. Math. (in press)] have obtained an interesting theorem for mappings satisfying a contractive condition of integral type. The aim of this note is to present a generalization of their main result.
Fixed points of weakly compatible mappings satisfying generalized $\varphi$-weak contractions
2014
In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a \(\varphi \)-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.