Tripled Fixed Point Results in Generalized Metric Spaces under Nonlinear Type Contractions Depended on another Function

Abstract

In 2006, Mustafa and Sims[18-19] introduced an improved version of the generalized metric space structure which they called G-metric spaces and in 2011; Berinde and Borcut [11] introduced the concept of triple fixed point. The intent of this paper is to establish some tripled fixed point theorems for mappings having mixed monotone property under nonlinear type contractions depended on another function in the framework of a G-metric space X enclosed with partial order. The presented results generalize, improve and extend corresponding results of Hassen et al. [13] ( Tripled Fixed Point Results in Generalized Metric Spaces” Journal of Applied Mathematics Volume 2012, Article ID 314279, 10 pages, doi:10.1155/2012/ 314279). Moreover, some examples are provided to illustrate the usability of the obtained results.

Keywords

• Tripled fixed point
• nonlinear contractions
• partially ordered sets
• G-metric spaces
• mixed monotone
• ICS mapping

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