In this paper, we initiate the notion of generalized multivalued $({\alpha }_K^{*},\mathsf{{\rm Y}},\mathsf{\Lambda })$ -contractions and provide some new common fixed point results in the class of ${\alpha }_K$ -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

In this paper, we initiate the notion of Ćirić type rational graphic $\left(\mathsf{{\rm Y}},\Lambda \right)$ -contraction pair mappings and provide some new related common fixed point results on partial b-metric spaces endowed with a directed graph G. We also give examples to illustrate our main results. Moreover, we present some applications on electric circuit equations and fractional differential equations.

The purpose of this paper is to generalize fixed point theorems introduced by Jleli et al. (J. Inequal. Appl. 2014:38, 2014) by using the concept of triangular α-orbital admissible mappings established in Popescu (Fixed Point Theory Appl. 2014:190, 2014). Some examples are given here to illustrate the usability of the obtained results.

Cubic Pythagorean fuzzy (CPF) set (CPFS) is a hybrid set that can hold much more information and can be used to describe both an interval-valued Pythagorean fuzzy set (IVPFS) and Pythagorean fuzzy set (PFS) at the same time to handle data uncertainties. Based on it, the present study is classified into three phases. The first phase is to modify the existing operational laws and aggregation operators (AOs) in the article presented by Abbas et al. (Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1529–1544, (2019)). The main objective of improved operational laws is to eliminate the flows and ambiguities in existing AOs. Secondly, based on these laws, various AOs to aggregate the information are acquired along with their requisite properties and relations. Lastly, an approach for interpreting the multi-attribute decision-making (MCDM) problem based on the stated operators is given and illustrated with an example. Some of the existing models are used to perform a comprehensive comparative analysis to demonstrate their impacts.

This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.