Abstract
In this paper, we introduce the notions of α -almost Istrăt̨escu contraction of type E and of type E ∗ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.
Highlights
Introduction and PreliminariesFixed point theory is an important tool in the investigation of the solutions of integral and differential equations via the successive approximations approach
One of the most significant fixed point result was given by Istrătescu [1]
The idea of Istrătescu [1] can be considered as a Second-Order Contraction Principle. We recall this interesting fixed point theorem of Istrătescu
Summary
Introduction and PreliminariesFixed point theory is an important tool in the investigation of the solutions of integral and differential equations via the successive approximations approach. Under the assumptions of Theorem 2, the mapping T has a unique the fixed point, provided that for any y ∈ M
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