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Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

Pakkaranang Nuttapol, Rehman Habib ur, Kumam Wiyada

Demonstratio Mathematica

2021

Vol. 54, nr 1

280--298

The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.

Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

Rehman Habib ur, Gopal Dhananjay, Kumam Poom

Demonstratio Mathematica

2019

Vol. 52, nr 1

166--182

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α-ψ and β-ψ con-densing operators and using them we propose new fixed point results. Our results generalize and extendsome comparable results from the literature. Additionally, as an application, we apply the obtained fixedpoint theorems to study the nonlinear functional integral equations.