In this manuscript, we introduce a new notion: a Berinde type $(\alpha ,\psi )$ -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given.

In the present paper the concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and q-rung \(( \alpha ,\beta ) \)-cuts are introduced. Some common fixed point results for q-ROF mappings are presented in b-metric spaces using Suzuki-type contractive conditions. Examples in support of obtained results are also presented. We have also presented an application of our result for the existence of solution of nonlinear fractional integral inclusion. The results are of their own kind in the literature of q-ROF sets and will pave the way for further research in the area.

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields of applied sciences. In the present article, a class of q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for a numerical solution of a distinct class of fractional differential inclusions have been achieved with the help of Schaefer type and Banach contraction fixed point theorems. A physical example is also provided to validate the hypothesis of the main results. The notion of q-rung orthopair fuzzy mappings along with the use of fixed point techniques and a new-fangled Caputo type fractional derivative are the principal novelty of this article.

This paper introduced a novel concept of q‐rung orthopair fuzzy (q‐ROF) metric spaces, in connection with the idea of q‐ROF sets, which generalizes well‐known concepts of fuzzy metric spaces and intuitionistic fuzzy metric spaces. An elaborated example has been provided representing the increase in selection space due to the q‐ROF metric and limitations for the case of intuitionistic fuzzy metric space. We have presented the definitions of introduced concepts along with examples, so they are way more understandable for readers. Some basic topological results have been defined and proved for q‐ROF metric space. The concept of q‐ROF Menger boundedness is introduced, and its application in game theory is presented. Also we have presented the significance of introduced metric compared to existing versions of fuzzy metric in the consequent sections. Baire’s theorem and uniform limit theorem are also established in the perspective of q‐ROF metric spaces. An application of the obtained results in the field of game theory is also presented to draw the attention of investigators searching new fields of research.

Authors have introduced fixed point results in the cone metric space. I have reviewed the manuscript; however, it lacks the following. 1: The abstract needs to be more comprehensive. 2: The layout of the manuscript needs to be improved. 3: The in...

In this manuscript, we introduce generalized hybrid mappings in hyperbolic metric spaces. We first show that the set of fixed points of such mappings is closed and convex. We then prove the existence of fixed point of these mappings and finally approximate the fixed point using Mann iterative process. We have also provided an example of generalized hybrid mappings in the setting of R-trees for the first time in the literature.