Vishal Joshi

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

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.

A novel framework of complex valued fuzzy metric spaces and fixed point theorems 1

In this article, recognizing the innovative concept of complex valued fuzzy set due to Ramot et al. (1) , we introduce the notion of complex valued fuzzy metric spaces. Several allied topological aspects for complex valued fuzzy metric spaces are also defined which fortify the concept. Moreover the complex valued fuzzy version of some celebrated and essential results from metric spaces including Banach contraction principle and the main theorem of Jungck (2) are established. Additionally some fixed point theorems satisfying certain rational expressions are proved.

ϕ-contractive multivalued mappings in complex valued metric spaces and remarks on some recent papers

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via -contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers Ahmad, Klin-Eam, and Azam (2013) and Kutbi, Ahmad, Azam, and Al-Rawashdeh (2014) based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested.