Fixed point theorems in <i>R</i>-metric spaces with applications

Single and Multivalued Maps on Parametric Metric Spaces Endowed with an Equivalence Relation

“…It is not wrong to say that the contraction condition given by Salimi et al in [1] is the most renowned condition of this decade, whereas on the account of metric spaces, we have many abstract forms like b-metric spaces [2][3][4][5], partial metric spaces [6,7], and partial b-metric spaces [8,9]. Recently, the notions of R-metric [10] and parametric metric spaces [11] have been initiated.…”

“…Khalehoghli et al [10] took a binary relation E on H and a simple metric d on H to define an R-metric space, denoted as ðH, d, B R Þ. They also said that a self map…”

Some New Aspects of Metric Fixed Point Theory

“…Recently, Gordji et al [17] introduced the notion of orthogonal sets and gave a new extension for the classical Banach contraction principle; more details can be found in [18][19][20]. Utilizing the structure of orthogonal metric spaces, which appeared in [18,19], and the binary relation used with a metric, in [21], Ali et al [22] introduced the notion of R -partial b-metric space and proved fixed point results in this space. Recently, Javed et al [23] studied fixed point results in fuzzy b-metric space using ordered-theoretic relation, which can also be seen in the work of Alam et al [24].…”

OnR-Partialb-Metric Spaces and Related Fixed Point Results with Applications

“…After looking into the structure of orthogonal metric spaces, introduced by [29,30], and the binary relation used with a metric, [31,32], we introduce the notion of R-partial b-metric spaces. We are also improving and generalizing the concept of orthogonal contractions in the sense of R -partial b-metric spaces and establish some fixed point theorems for the proposed contractions.…”

“…Theorem 11 [31]. If T is an R -preserving and R -continuous R -contraction on an R -complete R -metric space with h 0 ∈ H such that h 0 Rl for each l ∈ H .…”