In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.

     The operator ψ has been introduced as an associated set-valued set function. Although it has importance for the study of minimal open sets as well as minimal I-open sets. As a result of this study, we introduce minimal I^*-open sets . In this study, several characterizations of minimal I^*-open sets are also investigated. This study also discusses the role of minimal  I^*-open sets in the *-locally finite spaces. In an aspect of topological invariant, the homeomorphic images of minimal I^*-open set has been discussed here.

In this paper, we illustrate how to use the generalized homogeneous -shift operator  in generalizing various well-known q-identities, such as Hiene's transformation, the q-Gauss sum, and Jackson's transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

In this paper, we discuss the difference between classical and nonclassical symmetries. In addition, we found the non-classical symmetry of the Benjamin Bona Mahony Equation (BBM). Finally, we found a new exact solution to a Benjamin Bona Mahony Equation (BBM) using nonclassical symmetry.

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.