Fixed point theorems for Altman type mappings (Q1096210)

Let (X,d) be a metric space. A map \(f: X\to X\) is called a generalized contraction if d(fx,fy)\(\leq Q(d(x,y))\), for all x,y\(\in X\), where Q is a real valued function satisfying: (i) \(0<Q(s)<s\), for \(s\in (0,s_ 1],\) (ii) \(g(s)=(s/s-Qs)\) is nonincreasing and (iii) \(\int^{s_ 1}_{0}g(s)ds<+\infty.\) Some fixed point theorems and the coincidence theorems for generalized contractions are given. The obtained results generalize some earlier results of M. Altman, G. Jungck, B. Watson, B. Meade, C. Norris, V. N. Sehagal and R. Sen.