Abstract
Extension of Ciric’s (Proc. Amer. Math. Soc. N0. 45 (1974), 267 - 273) asymptotic fixed point theorem for quasi-contractions in T−orbitally complete metric spaces is obtained for the class of (δ, k)−weak contractions studied by Berinde (Carpath. J. Math. 19(1):7-22, 2003; Nonlinear Anal. Forum 9(1): 43-53, 2004). Our results are significant extensions of those of Ciric and Berinde mentioned above and numerous others in literature.
Highlights
AND PRELIMINARIESOrbitally complete metric spaces have been investigated by a number of researchers in connection with so many contractive conditions to obtain asymptotic fixed point theorems
In this praxis we prove asymptotic fixed point theorems for the class of (δ, k)−weak contractions as an extension of Ciric [7] result for quasi-contractions in T −orbitally complete metric spaces
(2) Equation (9) stresses the fact that whereas the orbit-size D[O(x, ∞)] of a quasi-contraction depends on an initial guess x ∈ X, the orbit size D[O(x, ∞)] of a (δ, k)−weak contraction may not depend on an initial guess x ∈ X, it depends on some images T kx, k = 0, 1, 2, ... of the initial guess x
Summary
AND PRELIMINARIESOrbitally complete metric spaces have been investigated by a number of researchers in connection with so many contractive conditions to obtain asymptotic fixed point theorems. 45 (1974), 267 - 273) asymptotic fixed point theorem for quasi-contractions in T −orbitally complete metric spaces is obtained for the class of (δ , k)−weak contractions studied by Berinde Complete metric spaces have been investigated by a number of researchers in connection with so many contractive conditions to obtain asymptotic fixed point theorems.
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