Fixed point theorems for Meir-Keeler condensing operators in partially ordered Banach spaces

Abstract

The purpose of this paper to build up the concept of a Meir-Keeler condensing and integral type condensing operators in partially ordered Banach spaces via the concept of a measure of noncompactness. We also provide a characterization of a Meir-Keeler condensing operators using the notion of $L$-functions in partially ordered Banach spaces. To attain these results, we relaxed the conditions of boundedness, closeness, and convexity of the set at the expense that the operatoris monotone and bounded. In addition, as an application, we apply these results to obtain coupled and tripled fixed theorems. Our results generalize and extend similarliterature results.