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Volume 34, Issue 1
Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems

Gopi Prasad & Deepak Khantwal

DOI: 10.4208/jpde.v34.n1.6

J. Part. Diff. Eq., 34 (2021), pp. 83-93.

Published online: 2021-01

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  • Abstract

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.

  • Keywords

Binary relation, $R$-lower semi-continuity, relational metric spaces.

  • AMS Subject Headings

47H10, 54H25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gopiprasad127@gmail.com (Gopi Prasad)

deepakkhantwal15@gmail.com (Deepak Khantwal)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-83, author = {Prasad , Gopi and Khantwal , Deepak}, title = {Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {1}, pages = {83--93}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/18556.html} }
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 -

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.

Prasad , Gopi and Khantwal , Deepak. (2021). Fixed Point Theorems in Relational Metric Spaces with an Application to Boundary Value Problems. Journal of Partial Differential Equations. 34 (1). 83-93. doi:10.4208/jpde.v34.n1.6
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