Common Fixed Point Theorems for Contractive Mappings of Integral Type in $G$-Metric Spaces and Applications

Abstract

Two common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type in G -metric spaces are demonstrated. The results obtained in this paper generalize and differ from a few results in the literature and are used to prove the existence and uniqueness of common bounded and continuous solutions for certain functional equations and nonlinear Volterra integral equations. A nontrivial example is included.

Some fixed point theorems on equivalent metric spaces

“…Hence, the fixed point theorems can be studied as homotopies, for details see [25,32]. In a similar way, a contractive condition of integral type can be rewrite with respect to the itself equivalent metric space, hence we can obtain new theorems related to results from [11,14,16,23,26,30,33].…”

“…[11]. In the last decade, the literature records many papers in which this type of contractive condition are studied, see for example [14,16,30,23,33] and reference therein.…”

A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

“…In [1], the authors tried to find the parametric solution of VIEs of the first kind. In [2], the authors presented a dynamical study of this problem for applying energy storage (see, for example, [3][4][5] and the reference therein). In [6,7], the system of VIEs with discontinuous kernels was illustrated.…”