Abstract
Abstract In this paper, we introduce the concept of multi-valued almost E-contractions. We then present some approximate fixed point and fixed point results for such mappings in metric spaces. Our results generalize and improve several well-known results in literature. We also provide several illustrative examples to compare our findings with some earlier results. An application to homotopy theory is given.
Highlights
In this paper, we introduce the concept of multi-valued almost E-contractions
We present some approximate xed point and xed point results for such mappings in metric spaces
Inspired by above mentioned results, in this paper, we rst introduce the concept of multi-valued almost E-contractions and prove an approximate xed point theorem for such mappings on incomplete metric spaces
Summary
Nadler [28] (see [12]) proved that every multi-valued contraction mapping with closed values in a complete metric space has at least one xed point. H(T(x), T(y)) ≤ θd(x, y) + LD(y, T(x)), ∀x, y ∈ X It is proved in [10] that every multi-valued weak contraction in a complete metric space has at least one xed point. Inspired by above mentioned results, in this paper, we rst introduce the concept of multi-valued almost E-contractions and prove an approximate xed point theorem for such mappings on incomplete metric spaces. This result extends and generalizes several approximate xed point results in the literature. We have e(T(y), T(x)) ≤ αd(x, y) + β|D(x, T(x)) − D(y, T(y))|, ∀x, y ∈ X
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