Abstract
In this paper, we prove expansion mapping theorems using the concept of compatible maps, weakly reciprocal continuity, R-weakly commuting mappings, R-weakly commuting of type ( A f ) Open image in new window, ( A g ) Open image in new window and ( P ) Open image in new window in metric spaces and in G-metric spaces.
Highlights
In this paper, we prove expansion mapping theorems using the concept of compatible maps, weakly reciprocal continuity, R-weakly commuting mappings, R-weakly commuting of type (Af ), (Ag) and (P) in metric spaces and in G-metric spaces
It is obvious that pointwise R-weakly commuting maps commute at their coincidence points and pointwise R-weak commutativity is equivalent to commutativity at coincidence points
He showed that in the setting of common fixed point theorems for compatible mappings satisfying contraction conditions, the notion of reciprocal continuity is weaker than the continuity of one of the mappings
Summary
We prove expansion mapping theorems using the concept of compatible maps, weakly reciprocal continuity, R-weakly commuting mappings, R-weakly commuting of type (Af ), (Ag) and (P) in metric spaces and in G-metric spaces. Definition ([ ], see [ ]) A pair of self-mappings (f , g) of a metric space (X, d) is said to be R-weakly commuting at a point x in X if d(fgx, gfx) ≤ Rd(fx, gx) for some R > .
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