Research Article Common Fixed Points of Four Maps Satisfying -Contraction on -Metric Spaces Muhammad Nazam, 1 Ma Zhenhua, 2,3 Sami Ullah Khan, 1,4 and Muhammad Arshad 1 1 Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan 2 Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China 3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 10001, China 4 Department of Mathematics, Gomal University D. I. Khan, Khyber Pakhtunkhwa 29050, Pakistan Correspondence should be addressed to Ma Zhenhua; mazhenghua 1981@163.com Received 16 October 2017; Accepted 7 December 2017; Published 28 December 2017 Academic Editor: Ahmad S. Al-Rawashdeh Copyright © 2017 Muhammad Nazam et al. 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. We manifest some common fxed point theorems for four maps satisfying C´ ır´ ıc type -contraction and Hardy-Rogers type - contraction defned on complete -metric spaces. We apply these results to infer several new and old corresponding results. Tese results also generalize some results obtained previously. We dispense examples to validate our results. 1. Introduction and Preliminaries Afer the famous Banach Contraction Principle, a large number of researchers revealed many fruitful generalizations of Banach’s fxed point theorem. One of these generalizations is known as -contraction presented by Wardowski [1]. Wardowski [1] evinced the fact that every -contraction defned on complete -metric space has a unique fxed point. Te concept of -contraction proved to be another milestone in fxed point theory and numerous research papers on - contraction have been published (see, e.g., [2–8]). Recently, Cosentino and Vetro [9] established a fxed point result for Hardy-Rogers type -contraction and Mınak et al. [10] presented a fxed point result for C´ ır´ ıc type generalized - contraction. In 1989, Bakhtin [11] investigated the concept of -metric spaces; however, Czerwik [12] initiated study of fxed point of self-mappings in -metric spaces and proved an analogue of Banach’s fxed point theorem. Since then, numerous research articles have been published comprising fxed point theorems for various classes of single-valued and multivalued operators in -metric spaces (see, e.g., [13–19]). We shall bring into use the idea of C´ ır´ ıc type -contrac- tion and Hardy-Rogers type -contraction comprising four self-mappings defned on -metric space. We present com- mon fxed point results for four self-maps satisfying C´ ır´ ıc type and Hardy-Rogers type -contraction on -metric space. We apply our results to infer several new and old results. We denote (0, ∞) by R + , [0, ∞) by R + 0 , (−∞, +∞) by R, and set of natural numbers by N. We bring back into reader’s mind some defnitions and properties of -metric. Defnition 1 (see [12]). Let  be a nonempty set and ≥1 be a real number. A function   :  ×  → [0, ∞) is said to be a -metric if, for all ,,∈, one has (  1)  =  if and only if   (, ) = 0, (  2)   (, ) =   (, ), (  3)   (, ) ≤ [  (, ) +   (, )]. In this case, the pair (,   ,) is called a -metric space (with coefcient ). Defnition 1 allows us to remark that the class of -metric spaces is efectually more general than that of metric spaces because a -metric is a metric when =1. Te following example describes the signifcance ofa -metric. Hindawi Journal of Function Spaces Volume 2017, Article ID 9389768, 11 pages https://doi.org/10.1155/2017/9389768