Research Article Common Fixed Point Results for Generalized    Contractive Mappings and Applications Kastriot Zoto 1 and Ilir Vardhami 2 1 Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania 2 Department of Mathematics, Faculty of Natural Sciences, University of Tirana, Tirana, Albania Correspondence should be addressed to Kastriot Zoto; zotokastriot@yahoo.com Received 21 February 2018; Accepted 17 April 2018; Published 3 June 2018 Academic Editor: Tomonari Suzuki Copyright © 2018 Kastriot Zoto and Ilir Vardhami. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A class of −   -admissible mappings and general type −   contraction mappings on -metric-like space are defned. Some fxed point results dealing with such a class of contractions are obtained. Te generalized contractions considered in this work cover and unify many particular types of contractions. Finally, we present application to the existence of solutions for a system of integral equations by means of -metric-like spaces. 1. Introduction Te study of new classes of spaces and their basic properties are always favorite topics of interest. Recently some authors have introduced some generalizations of metric spaces in several ways and have studied fxed point problems in these spaces, as well as their applications. In this context, Matthews [1] introduced the notion of partial metric space where self- distance of an arbitrary point needs not be equal to zero. Hitzler and Seda [2] and Amini-Harandi [3] made further generalizations under the name of dislocated, respectively, metric-like space. Further, Shukla et al. introduced in [4] the notion of 0− complete metric space. Tis concept was further extended by Alghamdi et al. [5] under the name of - metric-like spaces. Tis class of spaces has received signifcant attention lately. Also these generalizations have been associated with new and generalized classes of contractive mappings. In this direc- tion Samet et al. [6] introduced the concept of -admissible and −-contractive mappings, further extended to the (, )-contractive mappings, (,,)-contractive mappings, and −-admissible mappings. Many papers dealing with the above notions have been considered to prove fxed point results (e.g., see [7–25]). In this paper, following the above discussion, we intro- duce the notion of −  -admissible mapping and also introduce the concepts of ( −    ,) quasi-contractive mappings and rational (−   ,,) contractive mappings in the larger framework of -metric-like space. Te considered contractive conditions not only generalize the known ones but also include and unify a huge number of existing results on the topic in the corresponding literature. Finally, we apply the given results to obtain existence of solutions of integral equations. 2. Preliminaries Defnition 1 (see [8]). Let  be a nonempty set and ≥1 be a given real number. A mapping  :  ×  → [0, ∞) is called a -metric if, for all , ,  ∈ , the following conditions are satisfed: (i) (, ) = 0 if and only if =; (ii) (, ) = (, ); (iii) (, ) ≤ [(, ) + (, )]. Te pair (, ) is called a -metric space with parameter . Defnition 2 (see [26]). Let  be a nonempty set. A mapping :×→[0,∞) is called metric-like if, for all ,,∈, the following conditions are satisfed: Hindawi Journal of Function Spaces Volume 2018, Article ID 1282414, 11 pages https://doi.org/10.1155/2018/1282414