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Journal of Function Spaces
Volume 2017, Article ID 1649864, 14 pages
https://doi.org/10.1155/2017/1649864
Research Article

Existence Results for Integral Equations and Boundary Value Problems via Fixed Point Theorems for Generalized -Contractions in -Metric-Like Spaces

1Department of Mathematics, Jabalpur Engineering College, Jabalpur, India
2Department of Applied Sciences, NITTTR, Ministry of HRD, Govt. of India, Bhopal 462002, India
3Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

Correspondence should be addressed to Adrian Petru┼čel; or.julcbbu.htam@lesurtep

Received 25 June 2017; Accepted 19 September 2017; Published 19 November 2017

Academic Editor: Ahmad S. Al-Rawashdeh

Copyright © 2017 Vishal Joshi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we introduce some new classes of generalized -contractions and we establish certain fixed point results for such mappings in the setting of -metric-like spaces. Some examples will illustrate the results and the corresponding computer simulations are suggestive from the output point of view. A second purpose of the paper is to apply the abstract results in the study of the existence of a solution for an integral equation problem and for a boundary value problem related to a real life mathematical model, namely, the problem of conversion of solar energy to electrical energy. Our study is concluded with an open problem, related to an integrodifferential equation arising in the study of electrical and electronics circuit analysis.