الفهرس 
A constrained problemOnly 14 pages are availabe for public view
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Abstract
Mathematical modellingofreal-life problems usually results infunctional equation, the initial value problem of the differential equations andintegral equations. Many mathematical formulationof physical phenomena contain differential equations,functional equation and functional differential equations.The the oryofintegral operators,integral equations and differential equations are importantparts ofnonlinear analysis.It is caused by the fact that this the oriesare frequentlyapplicableinotherbranchesofmathematicsandin mathematical physics ,biology aswellindescribing problems connected withreal world Our aimin this the sisistoconsider the question of the existenceanduniquenessofsolu tions of the functional equations with parameterandconstrainedproblemofafunctional integrale quation. Differential andintegralequationsplayavitalroleinthefieldofnonlinear analysis. They provideama the matical frameworktodescribefundamentallawsinphysicsandchemistry In disciplineslikebiologyande conomics,differential equationsare commonl yemployedto model the dynamicsofintricate systems Severalresearchershavededicatedtheir workto the study of the seequations,asevidenced by references [2-5-6-9-10-16.