Search Results (6)

This study explores innovative insights into the realms of dynamic programming and fractional differential equations, situated explicitly within the framework of partial modular b-metric spaces enriched with a binary relation $\mathcal{R}$, proposing a novel definition for a generalized ${\gimel }_C$-type Suzuki $\mathcal{R}$-contraction specific to these spaces. By doing so, we pave the way for a range of relation-theoretical common fixed-point theorems, highlighting the versatility of our approach. To illustrate the practical relevance of our findings, we present a compelling example. Ultimately, this work aims to enrich the existing academic discourse and stimulate further research and practical applications within the field. Full article

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. Full article

The current study attempts to identify a new generalized metric space structure, referred to as partial modular $b-$metric, that extends both partial modular metric space via $b-$metric space and explains the topological aspects of the new space implementing examples. In addition, a new contraction mapping referred to as modified interpolative almost $\mathcal{E}-$type contraction is determined, which is an interpretation of interpolative contraction bestowed with almost contraction and $\mathcal{E}-$contraction as well as a simulation function and a fixed point theorem that encompass such mappings in the context of partial modular $b-$metric space is demonstrated. In conclusion, an example and an application that endorse the main theorem’s outcomes are offered. Full article

Electronic circuits/systems operating in harsh environments such as space are likely to experience faults or failures due to the impact of high-energy radiation. Given this, to overcome any faults or failures, redundancy is usually employed as a hardening-by-design approach. Moreover, low power and a small silicon footprint are also important considerations for space electronics since these translate into better energy efficiency, less system weight, and less cost. Therefore, the fault-tolerant design of electronic circuits and systems should go hand in hand with the optimization of design metrics, especially for resource-constrained electronics such as those used in space systems. A single circuit or system (also called a simplex implementation) is not fault-tolerant as it may become a single point of failure and is not used for a space application. As an alternative, a triple modular redundancy (TMR) implementation, which uses three identical copies of a circuit or system and a voter to perform majority voting of the circuits and systems outputs, may be used. However, in comparison with a simplex implementation, a TMR implementation consumes about 200% more area and dissipates 200% more power when circuits or systems are triplicated. To mitigate the area and power overheads of a TMR implementation compared to a simplex implementation, researchers have suggested alternative redundancy approaches such as selective TMR (STMR) insertion, partially approximate TMR (PATMR), fully approximate TMR (FATMR), and majority voting-based reduced precision redundancy (VRPR). Among these, VRPR appears to be promising, especially for inherently error-tolerant applications such as digital image/video/audio processing, which is relevant to space systems. However, the alternative redundancy approaches mentioned are unlikely to be suitable for the implementation of control logic. In this work, we analyze various redundancy approaches and evaluate the performance of TMR and VRPR for a digital image processing application. We provide MATLAB-based image processing results corresponding to TMR and VRPR and physical implementation results of functional units based on TMR and VRPR using a 28-nm CMOS technology. Full article

In the present paper, we introduce the notion of $C^{*}$-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, $C^{*}$-algebra-valued partial metric space, and $C^{*}$-algebra-valued modular metric space and discuss it with examples. Some fixed point results using $(\varphi ,\mathcal{MF})$-contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations. Full article

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed. Full article