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Abstract and Applied Analysis
Volume 2014, Article ID 519038, 11 pages
http://dx.doi.org/10.1155/2014/519038
Research Article

Some Integral Type Fixed Point Theorems for Non-Self-Mappings Satisfying Generalized -Weak Contractive Conditions in Symmetric Spaces

1Department of Mathematics, King AbdulAziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Aligarh Muslim Univeristy, Aligarh 202 002, India
3Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor, Uttar Pradesh 246701, India
4Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, Thailand

Received 10 January 2014; Accepted 10 March 2014; Published 7 April 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Marwan Amin Kutbi et al. This 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.

Abstract

The aim of this paper is to obtain some new integral type fixed point theorems for nonself weakly compatible mappings in symmetric spaces satisfying generalized -contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013) to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.