Journal of Mathematical Analysis and its Contemporary Applications
Volume:5 Issue: 1, Winter 2023

In this paper, various fixed point results on metric-like spaces are collected. Important findings from the beginning up to the recent developments are discussed. Hence, the aim of this paper is to motivate further research in the setting of quasi-metric spaces and related domains.

In this paper, by using t-norms, we define complex fuzzy subgroups and normal complex fuzzy subgroups and investigate some of their characteristics of them. Later we introduce and study their intersection and composition of them. Next, we define the concept of normality between two complex fuzzy subgroups under t-norms and obtain some properties of them. Finally, we describe the image and the inverse image of them under group homomorphisms.

The aim of this paper is to prove a common fixed point theorem of rational type contraction in the context of complex-valued b-metric spaces and generalise some results in the existing literature. Finally, We furnish an interesting example in support of our main results.

By using L'Hospital's rule for monotonicity, we provide an alternative proof of a monotonicity property of a certain function involving the exponential function. This new approach is very concise.

The objective of this paper is to solve conformable fractional Sturm-Liouville equations using one class of special polynomials and special functions introduced in [13]. Also, the connection between Mittag-Leffler functions and specialpolynomials are established and conformable fractional derivatives of certain Mittag-Leffler functions are determined.

In this paper, we establish algebraic bounds of the ratio type in nature for the natural exponential function $e^x$ involving two parameters, a and n, which become optimal as a tends to 0 or n tends to infinity. The proof is mainly based on Chebyshev's integral inequality and properties of the incomplete gamma function. Subsequently, we focus on the simple case obtained with n = 1, with comparisons to existing literature results. For the applications, we provide alternative proofs of inequalities involving ratio functions of trigonometric and hyperbolic functions. Graphics are given to illustrate the theory.