Available online at www.isr-publications.com/jmcs J. Math. Computer Sci., 18 (2018), 184–191 Research Article Journal Homepage: www.tjmcs.com - www.isr-publications.com/jmcs Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces Kanayo Stella Eke a,* , Bijan Davvaz b , Jimevwo Godwin Oghonyon a a Department of Mathematics, Covenant University, Canaanland, KM 10 Idiroko Road, P. M. B. 1023, Ota, Ogun State, Nigeria. b Department of Mathematics, Yazd University, Yazd, Iran. Abstract In this paper, we introduce a class of nonlinear contractive mappings in metric space. We also establish common fixed point theorems for these pair of non-self mappings satisfying the new contractive conditions in the convex metric space . An example is given to validate our results. The results generalize and extend some results in literature. Keywords: Convex metric space, nonlinear contractive mapping, non-self mapping, common fixed point, coincidentally commuting. 2010 MSC: 47H10. c 2018 All rights reserved. 1. Introduction and preliminary definitions The metrically fixed point theorems for contraction self-mappings have find applications in various areas in mathematics and economics. Many authors have proved the existence and uniqueness of common fixed points of contraction self mappings in metric spaces and its generalizations (see Karapinar [12], Abdeljawad et al. [2], Aydi et al. [6], Aydi et al. [7]). Much work have been done on the approximation of fixed points of contraction mappings (see [3, 14, 15]). Kirk [13] extended the metric space to metric space of hyperbolic type by placing Krasnoselskii’s result (for f α =(1 - α)I + αI for some α ∈ (0, 1)) in the framework of convex metric space. In convex metric spaces occur cases where the involved function is not necessarily a self-mapping of a closed subset. Assad [4] and Assad and Kirk [5] proved the first fixed point result for multivalued non-self mappings in a metric space (X, d). Many authors have studied the existence and uniqueness of fixed and common fixed point results for non-self contraction mappings, see ´ Ciri´ c[8], Imdad and Kumar [11], Rhoades [17], Sumitra et al. [18]. Throughout our consideration, we suppose that (X, d) is a metric space which contains a family L of metric segments (isometric images of real line segment) such that (a) each two points x, y ∈ X are endpoints of exactly one number seg[x, y] of L, and (b) if u, x, y ∈ X and if z ∈ seg[x, y] satisfies d(x, z)= λd(x, y) for λ ∈ [0, 1], then d(u, z) 6 (1 - λ)d(u, x)+ λd(u, y). (1.1) * Corresponding author Email address: kanayo.eke@covenantuniversity.edu.ng (Kanayo Stella Eke) doi: 10.22436/jmcs.018.02.06 Received 2017-08-11