Numerical Solution of a Quadratic Integral Equation through Classical Schauder Fixed Point Theorem

A Remark to the Schauder Fixed Point Theorem

In the paper some sufficient conditions are established in order that a continuous map have a fixed point. The results are related to those obtained by R. D. Nussbaum in [18], L. Górniewicz and D. RozpłochNowakowska in [12], S. Szufla in [21] and D. Bugajewski in [6]. The famous Schauder Fixed Point Theorem [20] has been generalized in various directions by using different methods. For referenc...

Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature

Hyers–Ulam–Rassias stability of impulsive Volterra integral equation via a fixed point approach

‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.

A Fixed Point Approach to Stability of a Quadratic Equation

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type f(x + y) + g(x − y) = h(x) + k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f .

Existence of Solutions for some Nonlinear Volterra Integral Equations via Petryshyn's Fixed Point Theorem

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.