Abstract: The purpose of this paper is to contribute to the development of the multidual Gamma function. For this aim, we start by defining the multidual Gamma and we propose a multidual analysis technics of in order to show a result regarding real Gamma function.

Abstract:The study of innovative sequences and series is important in several fields. In this article, we examine the convergence properties of a particular product series that offers adaptability through two parameters and two functions. Based on this analysis, we extend our investigation to a related series. Our main theorems are proved in detail and include several new intermediate results that can be used for other convergence analysis purposes. This is particularly the case for a generalized version of the Riemann sum formula. Several precise examples are presented and discussed, including one related to the gamma function.

Abstract: In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a binary relation. We accomplish this by generalizing several key notions from metric fixed point theory, such as completeness, closedness, continuity, g-continuity, and compatibility, to the relation-theoretic setting. We then use these generalized concepts to prove results on the existence and uniqueness of coincidence points, defined by two mappings acting on a metric space with a binary relation. As a consequence of our main results, we obtain several established metrical coincidence point theorems. We further provide illustrative examples that~demonstrate~the main results.