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**1 - 5**of**5**### ON MIXED NONLINEAR INTEGRAL EQUATIONS OF VOLTERRA-FREDHOLM TYPE WITH MODIFIED ARGUMENT

, 2009

"... In the present paper we consider the following mixed Volterra-Fredholm nonlinear integral equation with modified argument: u(t, x) = g t, x, u(t, x) ∫ t ..."

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In the present paper we consider the following mixed Volterra-Fredholm nonlinear integral equation with modified argument: u(t, x) = g t, x, u(t, x) ∫ t

### ON A NONSTANDARD VOLTERRA TYPE DYNAMIC INTEGRAL EQUATION ON TIME SCALES

"... Abstract. The main objective of the present paper is to study some basic qualitative properties of solutions of a nonstandard Volterra type dynamic integral equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integ ..."

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Abstract. The main objective of the present paper is to study some basic qualitative properties of solutions of a nonstandard Volterra type dynamic integral equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate on time scales. 1.

### GROWTH ESTIMATES ON MIXED VOLTERRA-FREDHOLM TYPE INTEGRAL INEQUALITIES

"... Abstract. In this paper we establish explicit estimates on some mixed Volterra-Fredholm type integral inequalities which can be used as tools in certain applications. Some applications are also given to illustrate the usefulness of the results. Key words: growth estimates, Volterra-Fredholm type, in ..."

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Abstract. In this paper we establish explicit estimates on some mixed Volterra-Fredholm type integral inequalities which can be used as tools in certain applications. Some applications are also given to illustrate the usefulness of the results. Key words: growth estimates, Volterra-Fredholm type, integral inequalities, partial differential equations, parabolic type, epidemic models. AMS Mathematics Subject Classification: 34K10, 35R10. 1.

### NEW BOUNDS ON CERTAIN FUNDAMENTAL INTEGRAL INEQUALITIES

"... (Communicated by S. Saitoh) Abstract. In the present note we derive new explicit upper bounds on some fundamental integral inequalities which can be used as tools in the study of a class of Volterra-Fredholm type integral equations. Some applications are also given to illustriate the usefulness of o ..."

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(Communicated by S. Saitoh) Abstract. In the present note we derive new explicit upper bounds on some fundamental integral inequalities which can be used as tools in the study of a class of Volterra-Fredholm type integral equations. Some applications are also given to illustriate the usefulness of one of our results. 1.

### Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel

"... In this work, We use numerical technique to reduce the Volterra-Fredholm integral equation to a linear system of Fredholm integral equations of the second kind and we apply the product Nystrom method to solve this system of integral equations to get the approx-imate solution of Volterra-Fredholm int ..."

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In this work, We use numerical technique to reduce the Volterra-Fredholm integral equation to a linear system of Fredholm integral equations of the second kind and we apply the product Nystrom method to solve this system of integral equations to get the approx-imate solution of Volterra-Fredholm integral equation. The results are compared with the exact solution of the integral equation. Keywords: Volterra-Fredholm integral equation, Hilbert kernel, product Nys-trom method, Numerical treatment.