J ℋ $\mathcal {J}\mathcal {H}$ -Operator Pairs of Type (R) with Application to Nonlinear Integral Equations

Abstract

In this paper, a new class of noncommuting mappings as J H-operator pairs of type (R) are introduced and some examples are presented. Also, a common fixed point theorem for this kind of mappings is proved. Finally, as an application, the existence of a solution of nonlinear integral equations is proved. Keywords Common fixed point · J H-operator pair · J H-operator pair of type (R) · Nonlinear integral equation Mathematics Subject Classification (2010) 47H09

Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications

“…Following the same steps from (29)- (33) with suitable changes and substituting (25), (34), (36) in 35, we have…”

“…These kinds of inequalities have many applications, when one wants to study the existence and uniqueness of the solutions of a differential equation (see [33][34][35]). The results of our research depend on the law that maxima are taken on the intervals [τ v, v], where 0 < τ < 1; however, previously in most papers, the maxima on the interval was held on [vn, v] and n > 0.…”

Fixed points of subadditive maps and some non-linear integral equations

“…The term integral equation was first used by Paul du Bois-Reymond in 1888. Recently, some researchers have been studied the problems of existence, uniqueness and other properties of solutions of some types of nonlinear integral equations, for example, see [10,1,7,12,13,14]. Let us consider the following Volterra integral equation: Thus all conditions of Theorem 3.2 are satisfied.…”

Fixed Points of Subadditive Maps with an Application to a System of Volterra–Fredholm Type Integrodifferential Equations

“…Recently, an attractive work on separating maps between different spaces of functions (as well as, operator algebras) is considered (see [14][15][16][17] and references therein). e existence, uniqueness, continuation, and other properties of solutions for nonlinear integral and integrodifferential equations are studied in [18][19][20][21][22][23][24][25]. e purpose of this work is to prove some new fixedpoint theorems for strongly subadditive maps and to ensure the existence and uniqueness of solutions for the following system of Volterra-Fredholm type integrodifferential equations:…”