College of Science

The first objectives of this thesis, is oriented towards function approximation using special type of spline, which is called the "G-spline" including the details of the subject and the proof of some lemmas and corollary for completeness. The second objective of this work is the generalization of G-spline functions for two-dimensional spaces including the statement and proof of the existence and uniqueness theorems as well as the statement and proof of the optimality of two-dimensional G-spline functions.

      The integral inequalities have many applications in the mathematics, applications in the ordinary differential equations, partial differential equations, integro-differential equations, fractional differential equations, etc. From these applications, finding the global existence, uniqueness, stability of solutions and other types of applications.