Condition In Complete Metric Space Research Articles

Error bounds revisited

We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuity in the case of sufficient conditions and (in some cases) convexity in the case of necessary conditions. We expose the roles of the assumptions involved in the error bound assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. Employing special collections of slope operators, we introduce a succinct form of sufficient error bound conditions, which allows one to combine in a single statement several different assertions: nonlocal and local primal space conditions in complete metric spaces, and subdifferential conditions in Banach and Asplund spaces.

On Some New Contractive Conditions in Complete Metric Spaces

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F:(0,+∞)→(−∞,+∞). According to the recently obtained results, this was possible (Wardowski’s method) only if two more properties (F2) and (F3) were used instead of the aforementioned strictly increasing (F1). Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α(u,v)=1 for every u and v from metric space Ξ, we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained.

Common Fixed Point Theorems For Weakly Compatible Mappings Satisfying Rational Contractive Conditions In Complete Metric Spaces

Common Fixed Point Theorems For Weakly Compatible Mappings Satisfying Rational Contractive Conditions In Complete Metric Spaces

Common fixed point for fuzzy mappings satisfying an implicit φ φ-contractive conditions in complete metric spaces

Common fixed point for fuzzy mappings satisfying an implicit φ φ-contractive conditions in complete metric spaces

Fixed points for cyclic φ-contractions in generalized metric spaces

AbstractIn this paper, we obtain a fixed point theorem for mappings satisfying cyclic φ-contractive conditions in complete metric spaces, which gives a positive answer to the question raised by Radenović (Fixed Point Theory Appl. 2015:189, 2015). We also find that this result and the fixed point result satisfying cyclic weak ϕ-contractions given by Karapınar (Appl. Math. Lett. 24:822-825, 2011) are independent of each other. Furthermore, when the number of cyclic sets is odd, we obtain fixed point theorems satisfying cyclic weak ϕ-contractions and cyclic φ-contractions in the setting of generalized metric spaces.

ON Modified(α-η)-Contractive Mappings

Hussain et al. (2013) established new fixed point results in complete metric space. In this paper, we prove fixed point results ofα-admissible mappings with respect toη, for modified contractive condition in complete metric space. An example is given to show the validity of our work. Our results generalize/improve several recent and classical results existing in the literature.

A Common Fixed Point Theorem for a Sequence of Multivalued Mappings

Recently, fixed point theorems for multivalued contraction mappings in metric spaces were obtained by many authors ( [5] , [2] , [7] , [1] , [4] , [6] , etc) . On the other hand, Dube [3] proved a theorem on common fixed points of two multivalued mappings. In this paper, we shall give a common fixed point theorem for a sequence of multivalued mappings satisfying some conditions in complete metric spaces. In our theorem, we shall obtain an extension of the result of Itoh [4] to the case of a sequence of multivalued mappings.