Fixed point theorems for integral G-contractions

Abstract

We define the notion of an integral G-contraction for mappings on metric spaces and establish some fixed point theorems for such mappings. Our results generalize and unify some recent results by Jachymski, Branciari and those contained therein. As an application, we obtain a result for cyclic operators. Moreover, we provide an example to show that our results are substantial improvements of some known results in literature. MSC: 47H10; 54H25

Some Fixed Point Theorems in -Metric Space Endowed with Graph

“…: → , and let ∈ , and the sequence { } in is such that → * with ( , +1 ) ∈ ( ) for ∈ N. One says that a graph is ( )-graph if there exists a subsequence { } and a natural number such that ( , * ) ∈ ( ) for all ≥ [23]. One says that a graph is ( )-graph if…”

Fixed point theorems under some contractive conditions in partial Hausdorff metric spaces

“…Further, in [6], he introduced the notion of Banach G-contractions. Then many authors extended the Banach G-contraction different from Jachymaski [15], [16], [17] and [18].…”

A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

“…Jachymski in [9], merged above theories to have a generalization of the Banach contraction principle for mappings of a metric space endowed with a graph. Then, Beg et al [3] extended some results of Jachymski to multivalued mappings; other generalizations of [9] are available in [1,4,5,10,15,17,18]. For completeness, we recall that Nadler [14] first extended the Banach contraction principle to multivalued mappings; then, Nadler's fixed point theorem has been generalized and extended in several directions, see for example [2, 6, 8, 11-13, 16, 19].…”