Abstract
Abstract The existence, uniqueness, and iterative approximations of fixed points for four classes of contractive mappings of integral type in complete metric spaces are established. The results presented in this paper generalize indeed several results of Branciari (J. Math. Math. Sci. 29(9):531-536, 2002), Rhoades (Int. J. Math. Math. Sci. 2003(63):4007-4013, 2003) and Liu et al. (Fixed Point Theory Appl. 2011:64, 2011). Four illustrative examples with uncountably many points are also included. MSC:54H25.
Highlights
Over the past decade the researchers [ – ] introduced a lot of contractive mappings of integral type and discussed the existence of fixed points and common fixed points for these mappings in metric spaces and modular spaces, respectively
Branciari [ ] was the first to study the existence of fixed points for the contractive mapping of integral type and proved the following result, which extends the Banach fixed point theorem
Theorem . ([ ]) Let f be a mapping from a complete metric space (X, d) into itself satisfying d(fx,fy) d(x,y) φ(t) dt ≤ c φ(t) dt, ∀x, y ∈ X
Summary
Over the past decade the researchers [ – ] introduced a lot of contractive mappings of integral type and discussed the existence of fixed points and common fixed points for these mappings in metric spaces and modular spaces, respectively. Branciari [ ] was the first to study the existence of fixed points for the contractive mapping of integral type and proved the following result, which extends the Banach fixed point theorem. Rhoades [ ] and Liu et al [ ] extended the result of Branciari and proved the following fixed point theorems.
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