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1

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

Pakkaranang Nuttapol, Rehman Habib ur, Kumam Wiyada

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

280--298

EN

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.

2

Some convergence results for nonlinear singular integral operators

Karsli H.

Demonstratio Mathematica

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2013

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Vol. 46, nr 4

729--740

EN

In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators Tλf of the form (...), acting on functions with bounded (Jordan) variation on an interval [a, b] as λ→λ0. Here, the kernels (...) satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].

3

Rotative mappings in metric spaces of hyperbolic type

Górnicki J., Pupka K.

Journal of Mathematics and Applications

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2006

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Vol. 28

49-70

EN

The aim of this paper is to give some conditions providing existence of fixed points for k-lipschitzian and uniformly k-lipschitzian mappings which are n-rotative with n ≥ 2 in complete metric spaces of hyperbolic type.

4

On bounded solutions of second order systems

Herzog G.

Demonstratio Mathematica

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2006

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Vol. 39, nr 4

793-801

EN

We prove existence and uniqueness of bounded solutions of u"+f(t, u) = 0, u(0) = x on [0,infinity) under quasimonotonicity and one-sided Lipschitz conditions on f.

5

Równania różniczkowe paraboliczne w pracach Profesora Piotra Besali

Kamont Z.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

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1999

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[Z] 35

55-80

6

Time-parametric control : uniform convergence of the optimal value functions of discretized problems

Gugat M.

Control and Cybernetics

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1999

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Vol. 28, no 1

7-33

EN

The problem of time-optimal control of linear hyperbolic systems is equivalent to the computation of the root of the optimal value function of a time-parametric program, whose feasible set is described by a countable system of moment equations. To compute this root, discretized problems with a finite number of equality constraints can be used. In this paper, we show that on a certain time-interval, the optimal value functions of the discretized problems converge uniformly to the optimal value function of the original problem. We also give sufficient conditions fot Lipschitz and Hoelder continuity of the optimal value function of the original problem.

7

On random Lipschitz condition and its application in approximation theory

Musielak J.

Fasciculi Mathematici

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1998

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Nr 28

119-125

EN

There are estimated moduli of continuity of functions satisfying Lipschitz condition with random exponents both in the sense of convergence in probability and convergence in mean. The results are applied to extend Jackson's direct approximation theorem to the case of Lipschitz condition with a random exponent.