The metric function generalizes the concept of distance between two points and hence includes the symmetric property. The aim of this article is to introduce a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. We show that our result is applicable to a class of mappings where neither the multivalued version of Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points. Application of our result to the solution of integral equations has been provided. A multivalued Reich type generalized version of the result is also established.

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results.

The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk–Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modified Ćirić-Reich–Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for $\omega$ -interpolative Ćirić-Reich–Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.

Efficient transportation and road network infrastructure plays the most significant role in the development of any region. However, the effectiveness of a road network is often affected by problems like road condition, traffic congestion, road blockage, road accidents etc. Digitization of the road network and its analysis can therefore be an effective tool towards resolving these issues. The free and open-source software Quantum Geographic Information System (QGIS) is well suited for such an analysis. QGIS can be used for construction of suitable road network maps of certain areas which provide sufficient information for such analysis. Cachar district of Assam, particularly Silchar circle, suffers frequently from traffic problems for being a network hub for other neighbouring revenue circles and some neighbouring north-eastern states. The scientific visualization and analysis of the road network of this district using GIS tools is still not available in literature. The results of the current study and their application could help the administrators and decisionmakers to build a sustainable road network. In this paper, we make an attempt to digitize the existing road network of Cachar district for its proper analysis. We compile the major and minor road density maps for the five revenue circles of the district. We use OpenStreetMap (OSM) to access and download existing road network in the district. Further, using the shortest path tool in QGIS, we find and display the shortest route between two junction points in the road network. Finding optimal route can be of great utility during emergency medical responses or fire or flood situations. Most of the major and minor roads within Cachar district were digitized in QGIS environment to perform the road network analysis.