Meir-Keeler Type n-tuplet Fixed Point Theorems in Partially Ordered Metric Spaces

Year 2014, Volume: 27 Issue: 3, 933 - 952, 01.03.2014

Manoj Ughade , R. Daherıya

Abstract

An n-tuplet fixed point is a generalization of the well-known concept of “coupled fixed point and tripled fixed point”. The intent of this paper is to introduce the concept of mixed strict monotone property and generalize Meir-Keeler contraction for mapping , where n is an arbitrary positive integer. Also establish an n-tuplet fixed point theorem for mappings under a generalized Meir-Keeler contraction in the setting of partially ordered metric spaces. Related examples are also given to support our main results. Our results are the generalizations of the results of B. Samet [8] and Hassen et al. [15]. Also as application, some results of integral type are given.

Meir-Keeler Type n-tuplet Fixed Point Theorems in Partially Ordered Metric Spaces

Abstract

An n-tuplet fixed point is a generalization of the well-known concept of “coupled fixed point and tripled fixed point”. The intent of this paper is to introduce the concept of mixed strict monotone property and generalize Meir-Keeler contraction for mapping , where n is an arbitrary positive integer. Also establish an n-tuplet fixed point theorem for mappings  under a generalized Meir-Keeler contraction in the setting of partially ordered metric spaces. Related examples are also given to support our main results. Our results are the generalizations of the results of B. Samet [8] and Hassen et al. [15]. Also as application, some results of integral type are given.

Keywords

n-tuplet fixed point, Meir-Keeler type contraction, mixed strict monotone property, partially ordered metric space

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