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 state of Sikkim in India has many steep slopes and has been susceptible to landslides. Since 1968 there have been innumerable losses of lives and properties due to landslides. There is an urgent need for advance assessment of degrees of vulnerability and delineation of the most vulnerable zone for shifting of the population and infrastructure to a safer zone. The identification and formulation of most suitable and acceptable method for such assessment is still nascent and research based. In this study, an attempt has been made to integrate the concept of Shannon's entropy with the information value-based statistical model to evaluate the landslide susceptibility in the study area and assess the improvement made through the integration of Shannon's entropy by comparing the results with the landslide susceptibility determined from the information value-based statistical model alone. Initially, the thematic layers pertaining to all the causative parameters were overlaid with the help of geographical information system that resulted in the formation of 78,256 numbers of polygons for each one of which landslide susceptibility was determined. For each polygon, the total landslide information value (TLIV) was computed as the summation of the landslide information values determined for the individual sub-categories present within the respective polygons. Again for each polygon, the Shannon's entropy value of the individual parameters was multiplied with the summation of the landslide information values of all the sub-categories present within the respective parameters. The product values computed for the different causative parameters were summed up to determine the total landslide information value with entropy (TLIV_e). Finally, the entire study area was categorized into five zones of landslides susceptibility based on the TLIV and TLIV_e, respectively. The prediction accuracy of the landslides determined based on the landslide susceptibility derived from TLIV_e was found to be significantly high (91 %) as compared to that derived from TLIV (85 %) indicating the potential contribution of Shannon's entropy in the improved delineation of the landslide susceptibility zones.

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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.

The aim in our article is to introduce the notion of statistical convergence and statistically Cauchy sequences in intuitionistic fuzzy n-normed linear spaces. The paper shows that some properties of statistical convergence of real sequences also hold for sequences in this space. Characterization for statistically convergent and statistically Cauchy sequences is also given. Further, the concept of statistical limit points and statistical cluster points are introduced and their relation with limit points of sequences have been investigated.