Search results for "Fixed point"
showing 10 items of 347 documents
Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems
2013
We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.
Remarks on G-Metric Spaces
2013
In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.
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 …
Multi-valued F-contractions and the solution of certain functional and integral equations
2013
Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.
Fixed point theorems for -contractive type mappings
2012
Abstract In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
Best proximity point theorems for rational proximal contractions
2013
Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.
Fixed point for cyclic weak (\psi, C)-contractions in 0-complete partial metric spaces
2013
In this paper, following (W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89), we give a fixed point result for cyclic weak (ψ,C)-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak (ψ,C)-contractions is also given.
Some fixed point results for multi-valued mappings in partial metric spaces
2013
Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.