The concept of M-metric generalizes both partial metric and conventional metric concepts. The aim of this paper is to investigate certain fixed and common fixed point results for generalized contractive mappings in Mmetric spaces. Moreover, we demonstrate the applicability of our results by providing specific examples. Our findings extend several existing results in the literature, broadening them from conventional metric spaces to M-metric spaces.

The main goal of this article is to investigate the existence of a unique positive definite common solution to a pair of matrix equations. Our focus will be on two particular types of matrix equation systems. In order to achieve our target, we take the help of elegant properties of Thompson metric on the set of all n × n Hermitian positive definite matrices. To proceed with this, we first derive a common fixed point result for a pair of mappings utilizing a certain class of control functions in a metric space. Then we obtain sufficient conditions to ensure a unique positive definite common solution to the equations. Finally, to validate our results, we provide numerical examples with diagrammatic representations of the convergence behavior of iterative sequences.

Throughout this manuscript, we investigate a new class of distance spaces, called EA,B-distance in which a number of fixed point results can be achieved with the EA,B-distance. Moreover, we offer a procedure for creating an extended b- metric from a metric by employing EA,B-distance. Furthermore, this concept and the primary results are illustrated with examples.

We study an integration theory on general measure spaces without imposing the convention infinity times zero equals zero. Our approach depends upon the premises concerning the countable additivity of the corresponding measure and the fact that the measure of the empty set is zero. An outstanding feature of this approach concerns the fact that all the results obtained in this paper are implied by the Third Littlewood’s principle and a Fundamental Theorem asserting that if a bounded real-valued function defined on a set of finite measure is measurable then it is integrable.

In this paper, we present a numerical study of a two-layer fluid flowing around a vertical hollow cylindrical structure. We analyze the effect of two-layer fluid in the presence of hollow cylindrical structure in the surface and internal wave modes. We consider a hollow cylinder within a two-layer fluid wherein the upper fluid is bounded by a free surface above and the lower fluid is bounded by an impermeable solid below. A matched eigenfunction expansion and separation of variables method are used to obtain the diffracted velocity potentials in the identified domains. The obtained diffracted velocity potential gives us the wave elevation at the surface and the internal wave modes. We present the wave elevations with different parameters of the device in various wave modes of motion, including surface waves and internal waves. It is observed that in the surface mode, the free surface elevation is higher than the interface elevation and the free surface and the interface elevations are in same phase whereas in the internal wave mode, the elevation at the interface is greater than that at the free surface.

In this study, we demonstrate that fixed points can occur in extended b-metric spaces that are not necessarily complete. We must employ a novel form of contraction conditions in order to relax the completeness criterion. It has been investigated how fixed points behave in both partially complete and orbitally complete spaces. We provide some instances to highlight our findings.

Inspired by Kirk’s pioneering work, we initiate the concept of Kannan type asymptotic contractions. Using two constructive lemmas, we establish a fixed point theorem for Kannan type asymptotic contractions. What’s more, we present a fixed point result for asymptotic contractions concerning the generalization of weakly Ciri´c type. This theorem generalizes and im- ´ proves the results for Kirk’s asymptotic contraction introduced by Suzuki and for Kannan type asymptotic contraction.