METHOD OF LIMIT RECURRENCE BY CONTRACTIVE MAPPING IN SOLVING A CLASS OF EXPONENTIAL KERNEL INTEGRAL EQUATIONS
Keywords:
operator mapping, contractive mapping, metric space, functional (0, 1), defined space, operator equation, mapping kernel, limit recurrence, approximate solution, unique fixed point, unique solution, zeroth approximation, the n -th approximationAbstract
A method of solving a class of exponential kernel integral equations is suggested, when a polynomialized term is added to the integral. The kernel is defined on the unit square. The analytical solutions are found using limit recurrence of the corresponding operator mapping which is contractive one. The unique fixed point (solution) is represented as the geometrical progression sum.References
http://en.wikipedia.org/wiki/Contraction_mapping.
http://en.wikipedia.org/wiki/Metric_map.
Romanuke V. V. Solving exactly the singular kernel integral equation with polynomialized added function by limit recurrence application // Volyn Mathematical Bulletin. Applied Mathematics Series. Issue 8 (17). – Rivne : RSGU, 2011. – P. 152–170.
Maleknejad K. Convergence of approximate solution of nonlinear Fredholm – Hammerstein integral equations / K. Maleknejad, K. Nouri, M. Nosrati Sahlan // Communications in Nonlinear Science and Numerical Simulation. – 2010. –Volume 15, Issue
– P. 1432–1443. 5. Romanuke V. V. Solving the simplest integral equation forms exactly on limit recurrence with applied their being contractive mappings // Collection of Scientific Papers of Applied Math and Computer Technologies Faculty of Khmelnytskyy National University. – 2010. – N 1 (3). – P. 51–70.
Alabau-Boussouira F. Exponential and polynomial stability of a wave equation for boundary memory damping with singular
kernels / F. Alabau-Boussouira, J. Prüss, R. Zacher // Comptes Rendus Mathematique. – 2009. – Volume 347, Issues 5–6. – P. 277–282.
Abdou M. A. On the solution of linear and nonlinear integral equation / M. A. Abdou // Applied Mathematics and Computation. – 2003. – Volume 146, Issues 2–3. – P. 857–871.
Altaç Z. Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions / Z. Altaç // Journal of Quantitative Spectroscopy and Radiative Transfer. – 2007. – Volume 104, Issue 3. – P. 310–325.
Kaper H. Integral operators generated by exponential integrals / H. Kaper // Journal of Mathematical Analysis and
Applications. – 1977. – Volume 59, Issue 2. – P. 216–226.
Qing-Hua Ma. Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations / Qing-Hua Ma, J. Pečarić // Journal of Mathematical Analysis and Applications. – 2008. – Volume 341, Issue 2. – P. 894–905.
Tatar N. On a large class of kernels yielding exponential stability in viscoelasticity / N. Tatar // Applied Mathematics and Computation. – 2009. – Volume 215, Issue 6. – P. 2298–2306.
