In this paper, we introduce a viscosity iterative process, which converges strongly to a common element of the set of fixed points of a pseudo-contractive mapping and the set of solutions of a monotone mapping. We also prove that the common element is the unique solution of certain variational inequality. The strong convergence theorems are obtained under some mild conditions. The results prese...

In [Coupled fixed points for a class of contractions in partially ordered spaces and applications, J. Comput. Anal. Appl. vol. 13, no. 6, (2011), 1123-1131], Jiandong Yin introduced the concept of a mixed g-comparable mapping F : X2 → X and proved coupled coincidence point theorems for a class of nonlinear contractive mappings. In this paper, we introduce the concept of a mixed g-comparable map...

where 0 < k < 1. The Banach Contraction Mapping Principle appeared in explicit form in Banach’s thesis in 1922 1 . For its simplicity and usefulness, it has become a very popular tool in solving existence problems in many branches of mathematical analysis. Banach contraction principle has been extended in many different directions; see 2–6 . In 1997Alber andGuerreDelabriere 7 introduced the con...

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

Probabilistic metric space was first introduced by Menger [6]. Later, there are many authors who have some detailed discussions and applications of a probabilistic metric space, for example, we may see Schweizer and Sklar [8]. Besides, there are many results about fixed point theorems in a probabilistic metric space with contractive types having appeared; we may see the papers [1–3, 9–12]. In t...

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two s...

We introduce and discuss several types of ?-?-contractive mappings on quasi-metric spaces. obtain some fixed point theorems in this setting present suitable examples to show the validity our approach results. Finally, we give a characterization doubly Hausdorff right K-sequentially complete spaces terms type having point.

In this paper, we investigate new solutions to the Rhoades' discontinuity problem on existence of a self-mapping which has fixed point but is not continuous at metric spaces. To do this, use number defined as n(x,y)=[d(x,y)]β[d(x,Ty)]α[d(x,Ty)]γ[(d(x,Ty)+d(x,Ty))/2]1−α−β−γ, where α , β γ ∈ ( 0,1 ) with + &lt; 1 and some interpolative type contractive conditions. Also, geometric properties Fix(T...