Fixed point theorems for F-expanding mappings

Abstract

Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012 introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space. MSC: Primary 47H10; secondary 54H25

F m -contractive and F m-expanding mappings in M-metric spaces

“…Similarly, it is not difficult to see most the results of [7] and [3] are direct consequences of our results.…”

“…In the Section 3, we introduce the concept of F m -expanding mappings. In Section 4 we show that the results of [7] and [3], are direct consequences of our results. In the last section, we present some open questions.…”

F-contractive type mappings in b-metric spaces and some related fixed point results

“…In [20] Górnicki defined F-expanding mappings and proved a fixed point theorem using the result in [46]. In a similar manner, we define new types of F-expanding mapping and prove a fixed point result in b-metric spaces.…”

“…The idea behind the following results is from the paper of Górnicki [20], in which he used the following lemma for metric spaces. It may be restated for b-metric spaces.…”

A Relation-Theoretic Expansion Principle

“…Theorem 1 has been extend and generalized in many directions (see [2,14,24,30,12,1,9,20,11,22,23] and references cited therein).…”