An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space

Abstract

We introduce the new idea of (α−θσ)-contraction in quasi-metric spaces in this paper. For these kinds of mappings, we then prove new fixed-point theorems on left K, left M, and left Smyth-complete quasi-metric spaces. We also apply our results to infer the existence of a solution to a second-order boundary-value problem.

Keywords

• quasi-metric space
• left K-Cauchy sequence
• α-admissible mapping
• fixed point