TY - JOUR
T1 - Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems
AU - Prasad , Gopi
AU - Khantwal , Deepak
JO - Journal of Partial Differential Equations
VL - 1
SP - 83
EP - 93
PY - 2021
DA - 2021/01
SN - 34
DO - http://doi.org/10.4208/jpde.v34.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/18556.html
KW - Binary relation, $R$-lower semi-continuity, relational metric spaces.
AB - <p style="text-align: justify;">In this paper, we establish fixed point theorems for generalized nonlinear
contractive mappings using the concept of ω-distance in relational metric spaces. Thus
we generalize the recent results of Senapati and Dey [J. Fixed Point Theory Appl. 19,
2945-2961 (2017)] and many other important results relevant to this literature. In order
to reveal the usefulness of such investigations, an application to first order periodic
boundary value problem are given. Moreover, we furnish a non-trivial example to
demonstrate the validity of our generalization over previous existing results.</p>