Solving nonlinear and dynamic programming equations on extended b-metric spaces with the fixed-point technique

Abdelkader Belhenniche1, Liliana Guran2, Sfya Benahmed3, Фернандо Лобо Перейра4
1Laboratoire des Études Pratiques en Sciences de Gestion et Sciences Commerciales, École Supérieure de Commerce, 42003, Kolea, Tipaza, Algeria
2Department of Pharmaceutical Sciences, “Vasile Goldiş” Western University of Arad, L. Rebreanu, no. 86, 310048, Arad, Romania
3École Nationale Polytechnique d’Oran Maurice Audin, B.P 1523 El M’naouer Oran, 31000, Oran, Algeria
4SYSTEC, Faculty of Engineering and Institute for Systems and Robotics, Porto University, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal

Tóm tắt

AbstractIn this article, we present an approach to solve a wide range of nonlinear equations formulated in extended b-metric spaces based on a new fixed-point theorem on these spaces. This research effort was motivated by challenges arising in solving pattern problems efficiently that can not be addressed by using standard metric spaces. Our approach relies on a novel common fixed-point theorem for Ćirić-type operators on extended b-metric spaces requiring only very weak assumptions that we present and derive in this article. The proposed approach is illustrated by applications asserting the existence and uniqueness of the solutions to Bellman equations, Volterra integral equations, and fractional differential equations formulated in extended b-metric spaces. Moreover, the obtained results provide general constructive recursive procedures to solve the above types of nonlinear equations.

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