Some New Aspects of Metric Fixed Point Theory

In this manuscript, we prove fixed point results in R m -metric spaces endowed with an amorphous binary relation. Moreover, we give an example to highlight the utility of our main results. Finally, we apply our result to examine the existence and uniqueness of the solution for a Fredholm integral equation.

[1]  S. Czerwik,et al.  Contraction mappings in $b$-metric spaces , 1993 .

[2]  Mehdi Asadi,et al.  New extension of p-metric spaces with some fixed-point results on M-metric spaces , 2014 .

[3]  H. Baghani,et al.  A fixed point theorem for a new class of set-valued mappings in $\mathrm{R}$-complete $($not necessarily complete$)$ metric spaces , 2017 .

[4]  S. Banach.  Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[5]  Vishal Gupta,et al.  Some coupled fixed point theorems in partially ordered S-metric spaces , 2015 .

[6]  Roger D. Maddux,et al.  Relation Algebras , 1997, Relational Methods in Computer Science.

[7]  N. Özgür,et al.  A new generalization of metric spaces: rectangular M-metric spaces , 2018, Mathematical Sciences.

[8]  M. Imdad,et al.  Fixed point results in Mν$M_{\nu }$-metric spaces with an application , 2019, Journal of Inequalities and Applications.

[9]  Satish Shukla,et al.  Partial b-Metric Spaces and Fixed Point Theorems , 2014 .

[10]  Mohammad Imdad,et al.  Fixed Point Results in Partial Symmetric Spaces with an Application , 2019, Axioms.

[11]  G. Jungck,et al.  Some novel fixed point theorems in partially ordered metric spaces , 2020 .

[12]  Hassen Aydi,et al.  Ordered-Theoretic Fixed Point Results in Fuzzy b-Metric Spaces with an Application , 2021 .

[13]  A. Alam,et al.  Relation-theoretic contraction principle , 2015 .

[14]  M. Gordji,et al.  Fixed point theorems in R-metric spaces with applications , 2020 .

[15]  Hassen Aydi,et al.  Control Fuzzy Metric Spaces via Orthogonality with an Application , 2021 .

[16]  Hassen Aydi,et al.  Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application , 2019, Mathematics.

[17]  M. Gordji,et al.  Fixed point theory in generalized orthogonal metric space , 2017 .

[18]  A. Amini-Harandi,et al.  Metric-like spaces, partial metric spaces and fixed points , 2012, Fixed Point Theory and Applications.

[19]  H. Aydi,et al.  On R -Partial b -Metric Spaces and Related Fixed Point Results with Applications , 2020 .

[20]  A Branciari,et al.  A fixed point theorem of Banach--Caccioppoli type on a class of generalized metric spaces , 2000, Publicationes Mathematicae Debrecen.

[21]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[22]  Madjid Eshaghi Gordji,et al.  On orthogonal sets and Banach fixed point theorem , 2017 .

[23]  S. G. Matthews,et al.  Partial Metric Topology , 1994 .