Abstract:
In this paper, we study Banach contractions in uniform spaces endowed with a graph and give some sufficient conditions for a mapping to be a Picard operator. Our main results generalize some results of [J. Jachymski, "The contraction principle for mappings on a metric space with a graph", Proc. Amer. Math. Soc. 136 (2008) 1359-1373] employing the basic entourages of the uniform space.

Abstract:
We prove the existence of common xed points of a generalizedcontraction / Zamrescu pair of maps in a complete cone metric space. Ourresults generalize the results of Huang anf Zhang [L-G. Huang, X. Zhang:Cone metric spaces and xed point theorems of contractive mappings, J. Math.Anal. Appl. 332 (2007) 1468{1476] and extend the results of Rezapour andHamlbarani [Sh. Rezapour, R. Hamlbarani: Some notes on the paper Conemetric spaces and xed point theorems of contractive mappings", J. Math.Anal. Appl. 345 (2008) 719{724].

Abstract:
We obtain some new fixed point theorems for a ( )-pair Meir-Keeler-type set-valued contraction map in metric spaces. Our main results generalize and improve the results of Klim and Wardowski, (2007). 1. Introduction and Preliminaries Let be a metric space, a subset of , and a map. We say is contractive if there exists such that, for all , The well-known Banach’s fixed-point theorem asserts that if , is contractive and is complete, then has a unique fixed point in . It is well known that the Banach contraction principle [1] is a very useful and classical tool in nonlinear analysis. Also, this principle has many generalizations. For instance, a mapping is called a quasi-contraction if there exists such that for any . In 1974, ？iri？ [2] introduced these maps and proved an existence and uniqueness fixed-point theorem. Throughout this paper, by we denote the set of all real numbers, while is the set of all natural numbers. Let be a metric space. Let denote a collection of all nonempty closed subsets of and a collection of all nonempty closed and bounded subsets of . The existence of fixed points for various multivalued contractive mappings had been studied by many authors under different conditions. In 1969, Nadler Jr. [3] extended the famous Banach contraction principle from single-valued mapping to multivalued mapping and proved the below fixed-point theorem for multivalued contraction. Theorem 1.1 (see [3]). Let be a complete metric space, and let be a mapping from into . Assume that there exists such that where denotes the Hausdorff metric on induced by ; that is, , for all and . Then has a fixed point in . In 1989, Mizoguchi-Takahashi [4] proved the following fixed-point theorem. Theorem 1.2 (see [4]). Let be a complete metric space, and let be a map from into . Assume that for all , where satisfies for all . Then has a fixed point in . In 2006, Feng and Liu [5] gave the following theorem. Theorem 1.3 (see [5]). Let be a complete metric space, and let be a multivalued map. If there exist , such that for any , there is satisfying the following two conditions:(i) ,(ii) . Then has a fixed point in provided that the mapping defined by , , is lower semicontinuous; that is, if for any and , , then . In 2007, Klim and Wardowski [6] proved the following fixed point theorem. Theorem 1.4 (see [6]). Let be a complete metric space, and let be a multivalued map. Assume that the following conditions hold:(i)the mapping defined by , , is lower semicontinuous;(ii)there exist and such that Then has a fixed point in . Recently, Pathak and Shahzad [7] introduced a new

Abstract:
The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semigroups on metric graphs.

Abstract:
In this paper we introduced the concepts of cyclic contraction on S- metric space and proved some fixed point theorems on S- metric space. Our presented results are proper generalization of Sedghi et al. [14]. We also give an example in support of our theorem.

Abstract:
In this paper, we present the generalization of B-contraction and C-contraction due to Sehgal and Hicks respectively. We also study some properties of C-contraction in probabilistic metric space.

Abstract:
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry, endowed with a noncommutative vector addition operation and with a modified version of ratio of three collinear points. This is the geometry of normed affine group spaces, a category which contains the ones of homogeneous groups, Carnot groups or contractible groups. In this category group operations are not fundamental, but derived objects, and the generalization of affine geometry is not based on incidence relations.

Abstract:
We introduce the notion of cone rectangular metric space and prove {sc Banach} contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.

Abstract:
The probabilistic metric space as one of the important generalization of metric space was introduced by K. Menger in 1942. In this paper, we briefly discuss the historical developments of contraction mappings in probabilistic metric space with some fixed point results. Keywords : Fixed point; Distribution function; t-norm; PM space; contraction mapping. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5425 KUSET 2011; 7(1): 79-91

Abstract:
In this paper, we give a generalization of Hicks type contractions and Golet type contractions on fuzzy metric spaces. We prove some fixed point theorems for this new type contractions mappings on fuzzy metric spaces.