Combining the approaches of functionals associated with h-concave functions
and fixed point techniques, we study the existence and uniqueness of a
solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) +
? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R)
denotes the space of all continuous functions on [0,T] equipped with
the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0,
T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued
functions in [0,T]xR.
The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space . Later on, we give some examples of applications of this type of results.
In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results.
The aim of this paper is to extend the results of Bhaskar and Lakshmikantham
and some other authors and to prove some new coupled fixed point theorems
for mappings having a mixed monotone property in a complete metric space
endowed with a partial order. Our theorems can be used to investigate a
large class of nonlinear problems. As an application, we discuss the
existence and uniqueness for a solution of a nonlinear integral equation.
The goal of this manuscript is to present a new fixed-point theorem on
θ
−
contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with
θ
−
contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).
In this paper, a nonlinear integral equation related to infectious diseases is investigated. Namely, we first study the existence and uniqueness of solutions and provide numerical algorithms that converge to the unique solution. Next, we study the lower and upper subsolutions, as well as the data dependence of the solution.
The purpose of this manuscript is to obtain some fixed point results under mild contractive conditions in fuzzy bipolar metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation was studied as a kind of applications.
On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation