On some fixed point theorems in generalized metric spaces

Mathematical Sciences Letters, 2014

In this paper, our purpose is to give a new generalization of Kannan's type and Chatterjea's type fixed point theorems in metric spaces. We have two main ideas. Our first idea is applying the logic of Choudhury [5] to the Kannan type contraction mappings, the second is applying the logic of Dutta and Choudhury [6] to the Kannan type contraction mappings and Chatterjea type contraction mappings.

In this paper we prove a fixed point theorem for -generalized contractions and obtain its consequences. KEYWORDS: D*-metric space,K-contraction,  − í µí±”í µí±’í µí±›í µí±’í µí±Ÿí µí±Ží µí±™í µí±–í µí± §í µí±’í µí±‘ í µí±í µí±œí µí±›í µí±¡í µí±Ÿí µí±Ží µí±í µí±¡í µí±–í µí±œí µí±› .

We obtain sufficient conditions for the existence of a unique fixed point of Reich and Rhoades type contractive conditions on generalized, complete, metric spaces dependent on another function. Our results generalize and extend some well-known previous results.

Mathematical Sciences, 2012

Brianciari [A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000) 31-37] initiated the notion of the generalized metric space as a generalization of a metric space in such a way that the triangle inequality is replaced by the "quadrilateral inequality", d(x, y) ≤ d(x, a) + d(a, b) + d(b, y) for all pairwise distinct points x, y, a and b of X. In this paper, we establish a fixed point result for weak contractive mappings T : X → X in complete Hausdorff generalized metric spaces. The obtained result is an extension and a generalization of many existing results in the literature.

Abstract and Applied Analysis, 2012

Lakzian and Samet (2010) studied some fixed-point results in generalized metric spaces in the sense of Branciari. In this paper, we study the existence of fixed-point results of mappings satisfying generalized weak contractive conditions in the framework of a generalized metric space in sense of Branciari. Our results modify and generalize the results of Laksian and Samet, as well as, our results generalize several well-known comparable results in the literature.

International Journal of Advanced Statistics and Probability, 2016

In this paper, we prove there exists a coupled fixed point for a set-valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G-metric.

Advances in Fixed Point Theory, 2016

In this paper, we introduce a new class Ψ1 of functions which are different from Ψ introduced by Hussain, Parvaneh, Samet and Vetro [9]. We define JS - Ψ1 - contraction for a single selfmap and prove the existence of fixed points. Also, we extend JS - Ψ1 - contraction to a pair of selfmaps and prove the existence of coincidence points and prove the existence of common fixed points by assuming the weakly compatible property. Further, we study the existence of common fixed points for a pair of weakly compatible selfmaps satisfying property (E. A). Examples are provided to illustrate our results.

In this paper we shall study the fixed point theory in generalized metric spaces (gms). One of our results will be a generalization of Kannan's fixed point theorem in the ordinary metric spaces, and Das's fixed point theorem in gms.

Creative Mathematics and Informatics, 2012

In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

2013

We introduce some generalizations of Prešić type contractions and establish some fixed point theorems for mappings satisfying Prešić-Hardy-Rogers type contractive conditions in metric spaces. Our results generalize and extend several known results in metric spaces. Some examples are included which illustrate the cases when new results can be applied while old ones cannot.