Solving nonlinear and dynamic programming equations on extended \(b\)-metric spaces with the fixed-point technique

DOI10.1186/s13663-022-00736-5OpenAlexW4311035432MaRDI QIDQ6103683

Liliana Guran, Abdelkader Belhenniche, Sfya Benahmed, Fernando Lobo Pereira

Publication date: 27 June 2023

Published in: Fixed Point Theory and Algorithms for Sciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13663-022-00736-5

zbMATH Keywords

nonlinear integral equationscommon fixed pointBellman's equationsingle-valued mappingsextended \(b\)-metric spacesfractional differential equations system

Mathematics Subject Classification ID

Operator theory (47-XX) General topology (54-XX)

Cites Work

• Some common fixed point results for rational type contraction mappings in complex valued metric spaces
• Boyd-Wong-type common fixed point results in cone metric spaces
• He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind
• Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method
• Numerical solution of linear Volterra integral equations system of the second kind
• A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations
• Block by block method for the systems of nonlinear Volterra integral equations
• On the decomposition method for system of linear equations and system of linear Volterra integral equations
• Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions.
• On some extension of optimal control theory
• New fixed point theorems for set-valued contractions in \(b\)-metric spaces
• A simple Taylor-series expansion method for a class of second kind integral equations
• Second order necessary conditions for optimal impulsive control problems
• Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations
• Common fixed points of almost generalized \((\psi,\phi)_s\)-contractive mappings in ordered \(b\)-metric spaces
• A generalization of \(b\)-metric space and some fixed point theorems
• Fixed points for multivalued Suzuki type \((\theta, \mathscr{R})\)-contraction mapping with applications
• On the traveling salesman problem restricted to inputs satisfying a relaxed triangle inequality
• A Note on Contractive Mappings
• A Generalization of Banach's Contraction Principle
• An Approach to Fixed-Point Theorems on Uniform Spaces
• Hamilton-Jacobi-Bellman Equation and Feedback Synthesis for Impulsive Control
• On Nonlinear Contractions
• The theory of dynamic programming
• The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials
• An algorithm for solving a nonlinear integro-differential equation
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