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The aim of this article is to obtain new solutions to the open question on the existence of a contractive condition which is strong enough to generate a fixed point or a common fixed point, but does not force the mapping to be continuous at that fixed point or a common fixed point. In this context some fixed point and common fixed point theorems are proved. Some useful examples are provided to support our results. An application related to the discontinuous functions involved neural networks is also established. [ABSTRACT FROM AUTHOR]

In this article we define multivalued R-weakly contractive multi-valued mappings in ordered cone metric spaces without assumption of normality on cone, and generalize many results existing in the literature. We provide applications to solutions of integral inclusions and give nontrivial examples to support our main theorem. [ABSTRACT FROM AUTHOR]

In this article the coincidence points of a self map and a sequence of multivalued maps are found in the settings of complete metric space endowed with a graph. A novel result of Asrifa and Vetrivel is generalized and as an application we obtain an existence theorem for a special type of fractional integral equation. Moreover, we establish a result on the convergence of successive approximation of a system of Bernstein operators on a Banach space. [ABSTRACT FROM AUTHOR]

We define the concept of βFL-admissible for a pair of L-fuzzy mappings and establish the existence of common L-fuzzy fixed point theorem. Our result generalizes some useful results in the literature.We provide an example to support our result. [ABSTRACT FROM AUTHOR]

We define the concept of βℱL-admissible for a pair of L-fuzzy mappings and establish the existence of common L-fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result.