Comparable nonlinear contractions in ordered metric spaces

Volume 10, Issue 4, pp 1652--1674 http://dx.doi.org/10.22436/jnsa.010.04.29

Publication Date: April 20, 2017 Submission Date: May 26, 2016

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Authors

Aftab Alam - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Qamrul Haq Khan - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Mohammad Imdad - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.

Abstract

In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g- continuity and compatibility to order-theoretic setting especially in ordered metric spaces and utilize these relatively weaker notions to prove some existence and uniqueness results on coincidence points for g-comparable mappings satisfying Boyd-Wong type nonlinear contractivity conditions. We also furnish some illustrative examples to demonstrate our results. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of an integral equation.

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Keywords

• Ordered metric space
• TCC property
• g-comparable mappings
• g-admissible mappings
• termwise monotone sequence.

MSC

•  47H10
•  54H25

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