Abstract:
The main purpose of this paper is to obtain fixed points for a selfmap $T$ of a metric space which is $T$-orbitally complete under a more general contraction type condition by using a certain continuous control function. Further generalization relating to the diameter of orbits is given.

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 introduce local power contractions and nodal contractions in cone metric spaces and prove the existence of fixed points of such contractions in cone metric spaces. Our theorems generalize the results of Haung and Zhang [L-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476].

Abstract:
In developing countries like India, Industrialization is rising rapidly, and also？a great paucity of land is there, the demand for exploitation of industrial？wastes？which coming from industries is increasing. From geotechnical perspective,？fly ash, granite and quarry waste, cement kiln dust, silica fume, rice husk etc.？are the waste materials？which？have effectual features requisites by an excellent soil stabilization admixture. Stabilization using solid wastes is one of the different？methods of treatment, to improve the engineering properties and make it？suitable for construction. This paper briefs about the recent trends in stabilization of expansive soil using industrial waste (granite and quarry waste, cement kiln？dust, silica fume, rice husk) as stabilizers for decreasing the environmental？hazards.

Abstract:
We introduce two new classes of implicit relations and where is a proper subset of , and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in . These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation , where . Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation. 1. Introduction Existence of fixed point theorems in partially ordered metric spaces with a contractive condition has been considered by several authors (see [1–6]). Guo and Lakshmikantham [7] introduced mixed monotone operators. Gnana Bhaskar and Lakshmikantham [8] established the existence of coupled fixed points of mappings satisfying mixed monotone property in partially ordered metric spaces. Later, Lakshmikantham and Ciric [9] extended this property to two maps by introducing mixed -monotone property and established the existence of coupled coincidence point and coupled common fixed points for a pair of commuting maps. Choudhury and Kundu [10] extended the existence of coupled coincidence and coupled common fixed points for a pair of noncommuting maps, particularly for a pair of compatible maps. Definition 1 (see [7]). Let be a nonempty set. An element in is called a coupled fixed point of the mapping if and . A point is called a fixed point of if . Definition 2 (see [7]). Let be a partially ordered set and be a mapping. We say that satisfies mixed monotone property if is monotone nondecreasing in and monotone nonincreasing in ; that is, for any : Theorem 3 (see [8]). Let be a partially ordered set and suppose that is a metric on such that is a complete metric space. Let be a mapping satisfying mixed monotone property. Assume that there exists a with Suppose that either is continuous or the following conditions hold in : (i)if a nondecreasing sequence with , then for all and(ii)if a nonincreasing sequence with , then for all . If there exist such that and then has a coupled fixed point. In 2011, Luong and Thuan [11] proved the following coupled fixed point theorem. Theorem 4 (see [11]). Let be a partially ordered set and suppose that is a metric on such that is a complete metric space. Let be a mapping

Abstract:
With the new theoretical approach i.e. lie algebraic approach, we have calculated the infrared spectra of Phosphine in the range from 3000 cm^{-}^{1} to 9500 cm^{-}^{1} and Nitrogen Trifluoride in the range from 900 cm^{-}^{1} to 4500 cm^{-}^{1}. The model Hamiltonian, so constructed, seems to describe the P-H and N-F stretching modes accurately with only four numbers of parameters.

Abstract:
We prove that the convergence of the Mann iteration with modified errors is equivalent to the convergence of the Ishikawa iteration with modified errors for the class of uniformly continuous and strongly pseudocontractive maps. Our results improve the results of Soltuz [14] and extend the results of Rhoades and Soltuz [12] to the iterations with modified errors.

Abstract:
The purpose of this paper is to show that the Mann iteration converges faster than the Ishikawa iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a Banach space.

Abstract:
The purpose of this paper is to show that the Mann iteration converges faster than the Ishikawa iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a Banach space.