Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces

The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space ( X , { | ⋅ | p } p ∈ Λ ) (X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda}) having the 𝜏-Krein–Šmulian property, where 𝜏 is a weaker Hausdorff locally convex topology of 𝑋. The method applied in our study is connected with a family Φ Λ τ \Phi_{\Lambda}^{\tau} -MNC of measures of weak noncompactness and with the concept of 𝜏-sequential continuity. As a special case, we discuss the existence of solutions for a 2 × 2 2\times 2 block operator matrix with nonlinear inputs. Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space C ⁢ ( R + ) × C ⁢ ( R + ) C(\mathbb{R}^{+})\times C(\mathbb{R}^{+}) to verify the effectiveness and applicability of our main result.

Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

Using the idea of modified ϱ -proximal admissible mappings, we derive some new best proximity point results for ϱ − ϑ -contraction mappings in metric spaces. We also provide some illustrations to back up our work. As a result of our findings, several fixed-point results for such mappings are also found. We obtain the existence of a solution for nonlinear integral equations as an application.

Quasi-Newtonian methods for modeling of plan curve

The paper is devoted to the methods of geometric modeling of plane curves given in the natural parameterization. The paper considers numerical modeling methods that make it possible to find the equation of curvature of the desired curve for different cases of the input data. The unknown curvature distribution coefficients of the required curve are determined by solving a system of nonlinear integral equations. Various numerical methods are considered to solve this nonlinear system. The results of computer implementation of the proposed methods for modeling two curvilinear contours with different initial data are presented. For the first curve, the input data are the coordinates of three points, the angles of inclination of the tangents at the extreme points and the linear law of curvature distribution. The second example considers an S-shaped curve with a quadratic law of curvature distributi.

Integral Equations: Theories, Approximations, and Applications

Linear and nonlinear integral equations of the first and second kinds have many applications in engineering and real life problems [...]