Common Coupled Fixed Point Theorems for Geraghty - Type Contraction Mappings Using Monotone Property in Partially Ordered Partial b-Metric Spaces

K. P. R. Sastry, K. K. M. Sarma, Ch. Srinivasa Rao, Vedula Perraju

Abstract: In this paper, we prove common coupled fixed point theorems for Geraghty - type contraction mappings using monotone property in partially ordered partial b - metric spaces. We also to study the existence and uniqueness of coupled fixed points using monotone property instead of the often used mixed monotone property. Supporting example is also provided. An open problem is given at the end of the paper.

Keywords: Coupled fixed point, mixed monotone property, monotone property, partial b - metric, complete partially ordered partial b - metric space, Geraghty - type contraction