The aim of this paper is to introduce two classes of generalized α-ψ-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature. MSC: 54H25; 47H10; 54E50

In this paper, we introduce a new class of expansive mappings called generalized (ξ , α)-expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results. MSC: 46T99; 54H25; 47H10; 54E50 Keywords: expansive mapping; complete metric space; fixed point IntroductionFixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models (integral and partial differential equations, variational inequalities etc.). After the celebrated results of Banach [], fixed-point theory became one of the most interesting topics in nonlinear analysis. Consequently, a number of the papers have appeared since then; see e.g. +∞ n= ψ n (t) < +∞ for each t > , where ψ n is the nth iterate of ψ .(ii) ψ is non-decreasing. for all x, y ∈ X.

A new, simple and unified approach in the theory of contractive mappings was recently given by Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165 by using the concepts of α-ψ-contractive type mappings and α-admissible mappings in metric spaces. The purpose of this paper is to present a new class of contractive pair of mappings called generalized α-ψ contractive pair of mappings and study various fixed point theorems for such mappings in complete metric spaces. For this, we introduce a new notion of α-admissible w.r.t g mapping which in turn generalizes the concept of g-monotone mapping recently introduced byĆirić et al. (Fixed Point Theory Appl. 2008, Article ID 131294, 11 pages). As an application of our main results, we further establish common fixed point theorems for metric spaces endowed with a partial order as well as in respect of cyclic contractive mappings. The presented theorems extend and subsumes various known comparable results from the current literature. Some illustrative examples are provided to demonstrate the main results and to show the genuineness of our results.

The aim of this paper is to introduce classes of α-admissible generalized contractive type mappings of integral type and to discuss the existence of fixed points for these mappings in complete metric spaces. Our results improve and generalize fixed point results in the literature. MSC: 46T99; 54H25; 47H10; 54E50

In this paper, we consider a common fixed point result in the context of a very recently defined abstract space: "function weighted metric space". We present also some examples to illustrate the validity of the given results.