... case, an existence result is obtained by applying the Bohnenblust–Karlin’s fixed point theorem. For the second case, a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler is used. Further, an illustrating example is presented. Design/methodology/approach In Section 2, we...

... Leibnitz rule. Design/methodology/approach Firstly, we find a suitable integral representation of the solutions of the considered class of equations. Then, we construct two operators so that any fixed point of their sum is a solution of the considered nonlinear Volterra integro-dynamic equations...

... and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments. Design/methodology...

...Godwin Amechi Okeke; Daniel Francis Purpose This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al...

... ∈ C A sequence x n ⊂ C is an approximating fixed point sequence of T if lim n → ∞ ‖ x n − T x n ‖ = 0 . We say that x ∈ C is a fixed point of T if T ( x ) = x and denote F ( T ) the set of all...

...Godwin Amechi Okeke; Daniel Francis Purpose The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type...

...Adrian Magdaş The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate...

... general convex combinations, so we need some convex structure in a metric space to define an IMR on a nonlinear domain. where t n ∈ ( 0 , 1 ) and T : H → H is a nonexpansive mapping and established weak convergence of (1.2) to the fixed point of T under...