Fixed point theorems for Altman type mappings
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.
scientific article; zbMATH DE number 4030493