Existence of solution for two dimensional nonlinear fractional integral equation by measure of noncompactness and iterative algorithm to solve it

Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

“…By unifying and enlarging the earlier results of [12,15,29,34] and using Petryshyn's fixed point, we obtained a new method to prove the existence of solutions for some functional integral equations. The merit of Theorem 3.1 among the others (Darbo's and Schauder fixed point theorem) lies in that in applying this theorem, here one does not need to confirm the involved operator maps is on a closed convex subset onto itself.…”

“…They are often applied to the theories of Hadamard-type fractional integral operators and they find relations of the obtained results with earlier results about integral operators on different function spaces as well as the operator theory and geometry of Banach spaces (see [9,23,24,[30][31][32]). Numerous papers have been attached to the problem for the existence of solution of FIEs and infinite systems of integral equations in two variables in the different space (see [4,5,[12][13][14]21,29]). Here, we will study the following equation z(s, t) = f (s, t, z(ϕ 1 (s, t)), ..., z(ϕ k (s, t)) + F s, t, s 0 t 0 g(s, t, u, v, z(β 1 (u, v)), ..., z(β n (u, v)))dvdu, z(γ 1 (s, t)), ..., z(γ m (s, t)) × h(s, t, z(θ 1 (s, t)), ..., z(θ r (s, t))…”

“…Several authors examined an equation similar to (1) and their basic and good idea was the construction of an MNC with Darbo's fixed point theorem in the Banach algebra C[0, a] (see [4,5,15,29,34]). In our study, we apply Petryshyn's theorem (prefer over Darbo's theorem) to examine the solvability of Eq.…”

Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

“…First, we would be interested in studying some particular problems, such us Fredholm integral equations with non-singular kernels. Second, we would like to generalize our study to other integral equations, especially to nonlinear integral equations [17,18].…”

Extension of Darbo’s fixed point theorem via shifting distance functions and its application

“…Different real-life situations, which are modeled via FIEs, can be studied using FPT and measure of noncompactness (MNC) (see [2,3,5,7,10,11,13,19,21,[23][24][25][26]).…”