Solution of Some Impulsive Differential Equations via Coupled Fixed Point

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

[1]  K. Kalyani,et al.  Coupled fixed point theorems with rational expressions in partially ordered metric spaces , 2020, The Journal of Analysis.

[2]  Mehdi Mrad,et al.  Some Fixed Point Results on Rectangular Metric-Like Spaces Endowed with a Graph , 2019, Symmetry.

[3]  W. Shatanawi,et al.  Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction , 2013, Fixed Point Theory and Applications.

[4]  Vahid Parvaneh,et al.  Coupled coincidence point results for (ψ,φ)-weakly contractive mappings in partially ordered Gb-metric spaces , 2013 .

[5]  Wasfi A. Shatanawi,et al.  On w-compatible mappings and common coupled coincidence point in cone metric spaces , 2012, Appl. Math. Lett..

[6]  Jonas Gloeckner,et al.  Impulsive Differential Equations , 2016 .

[7]  Vasile Berinde,et al.  Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces , 2011, 1103.5285.

[8]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[9]  M. Mrad,et al.  On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph , 2019 .

[10]  Florin Bojor.  Fixed points of Kannan mappings in metric spaces endowed with a graph , 2012 .

[11]  Coupled Fixed Points of monotone mappings in a metric space with a graph , 2018, 1801.07675.

[12]  S. Chandok,et al.  COUPLED COMMON FIXED POINT RESULTS FOR MIXED g-MONOTONE MAPPS IN PARTIALLY ORDERED G-METRIC SPACES , 2013 .

[13]  Some new results on common coupled fixed points of two hybrid pairs of mappings in partial metric spaces , 2019, Journal of Nonlinear Functional Analysis.

[14]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[15]  Generalized contractions in metric spaces endowed with a graph , 2012 .

[16]  S. Saejung,et al.  Fixed point theorems for contractions of Reich type on a metric space with a graph , 2018 .

[17]  Ismat Beg,et al.  The contraction principle for set valued mappings on a metric space with a graph , 2010, Comput. Math. Appl..

[18]  New results on coupled fixed point theory in metric spaces endowed with a directed graph , 2014 .

[19]  W. Shatanawi,et al.  Some coupled fixed point theorems in quasi-partial metric spaces , 2013, Fixed Point Theory and Applications.

[20]  S. Czerwik,et al.  Nonlinear set-valued contraction mappings in b-metric spaces , 1998 .

[21]  Florin Bojor.  Fixed point of φ-contraction in metric spaces endowed with a graph , 2010 .

[22]  V. Lakshmikantham,et al.  Fixed point theorems in partially ordered metric spaces and applications , 2006 .

[23]  Nguyen Van Luong,et al.  Coupled fixed points in partially ordered metric spaces and application , 2011 .

[24]  M. Pitchaimani,et al.  New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov process , 2018, Transactions of A. Razmadze Mathematical Institute.

[25]  Johnny Henderson,et al.  Impulsive Differential Inclusions: A Fixed Point Approach , 2013 .

[26]  J. Jachymski,et al.  The contraction principle for mappings on a metric space with a graph , 2007 .

[27]  Lorentz Jäntschi,et al.  Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error , 2016, Comput. Math. Methods Medicine.

[28]  Florin Bojor.  Fixed point theorems for Reich type contractions on metric spaces with a graph , 2012 .

[29]  Zead Mustafa,et al.  Some common fixed point results of graphs on b -metric space , 2016 .

[30]  Wasfi Shatanawi,et al.  Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces , 2020, Mathematics.