Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

Some notes on PD-operator pairs

This paper points out several remarks on the paper of Pathak and Rai[H. K.Pathak and D. Rai, Common fixed point theorems for PD-operator pairs under relaxed con-ditions with applications, Journal of Computational and Applied Mathematics 239 (2013)103-113]. In fact, under contractive conditions (assumed in the above paper), proving existence of common fixed point by assuming the notion of PD-operator is equivalent to proving the existence of common fixed point by assuming the existence of common fixed point

A three point extension of Chatterjea's fixed point theorem with at most two fixed points

In this paper, we introduce a new category of mappings within metric spaces, specifically focusing on three-point analogs of the well-established Chatterjea type mappings. We demonstrate that Chatterjea type mappings and their three-point analogs are different classes of mappings. A fixed point theorem for generalized Chatterjea type mappings is established. It is shown that these mappings are continuous at fixed point. Connections between generalized Chatterjea type mappings, generalized Kannan type mappings, Chatterjea type mappings, and mappings contracting perimeters of triangles are found. Additionally, we derive two fixed point theorems for generalized Chatterjea type mappings in metric spaces, even when completeness is not mandatory.Comment: 16 pages, submitted to a journal on 11 January 2024. arXiv admin note: text overlap with arXiv:2308.0541