in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

The purpose of this paper is to present data dependence results for some multivalued weakly Picard operatorors such as: Reich-type operators, graphic-contractions.

In this paper we prove some existence theorems concerning the solutions and integral solution for functional (delay) evolution equations with nonconvex lower semicontinuous multivalued perturbations ,

In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when domA 6= R and domA = R , with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come f...

In this paper, we establish existence and uniqueness results for a new class of boundary value problems involving the ?-Hilfer generalized proportional fractional derivative operator, supplemented with mixed nonlocal conditions including multipoint, integral multiorder operators. The given problem is first converted into an equivalent fixed point problem, which then solved by means standard the...

In this paper, we introduce a new class of variational inequalities involving two operators. Using the projection technique, we establish the equivalence between the multivalued general variational inequalities and the fixed point problems. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the multivalued general variational inequalities. We also d...

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

In this paper, using the concept of measure of noncompactness, which is a very useful and powerful tools in nonlinear functional analysis, metric fixed point theory and integral equations, we introduce a new contraction on a Banach space. For this purpose by using of a measure of noncompactness on a finite product space, we obtain some generalizations of Darbo’s fixed-point theorem. Then, with ...

Recommended by Massimo Furi We obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contrac-tive condition of integral type. The results of this paper essentially contain every theorem on hybrid and multivalued self-maps of a metric space as a special case. under the Creative Commons A...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...