Abstract
In this article, we define a tangential property which can be used not only for single-valued mappings but also for multi-valued mappings, and used it in the prove for the existence of a common fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. Our theorems generalize and unify main results of Pathak and Shahzad (Bull. Belg. Math. Soc. Simon Stevin 16, 277-288, 2009) and several known fixed point results.
Highlights
The Banach Contraction Mapping Principle, appeared in explicit form in Banach’s thesis in 1922 [1] where it was used to establish the existence of a solution for an integral equation
In 1969, the Banach’s Contraction Mapping Principle extended nicely to setvalued or multivalued mappings, a fact first noticed by Nadler [6]
If the following conditions (a)-(d) holds: (a) there exists a point z Î f(X) ∩ g(X) which is a weak tangent point to (f, g), (b) (f, g) is tangential w.r.t (A, B), (c) f fa = fa, ggb = gb and Afa = Bgb for a Î C(f, A) and b Î C(g, B), (d) the pairs (f, A) and (g, B) are weakly compatible
Summary
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