Common Fixed Point Theorems For A Pair Of Weakly Increasing/Decreasing Self Maps Under $\psi$-Weak Generalized Geraghty Contractions in Partially Ordered Partial b-Metric Spaces

Abstract

In this paper we consider the concept of $\psi-$ weak generalized Geraghty contractive pair of weakly increasing/decreasing self mappings in a complete partially ordered partial b-metric space. We study the existence of fixed points for such a pair of weakly increasing/decreasing self mappings in complete partially ordered partial b-metric spaces controlled by $\psi-$ weak generalized Geraghty contractive type condition and obtain some fixed point results of G.V.R.Babu et.al [3] in complete partially ordered metric spaces as corollaries. Supporting example is also provided. An open problem is given at the end of the paper.