The aim of this manuscript is to introduce the concept of fuzzy b-metric-like spaces and discuss some related fixed point results. Some examples are imparted to illustrate the feasibility of the proposed methods. Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral equations.

This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially $ s $-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex function have been established. Additionally, some special cases of the newly established results are derived as well. Finally, as applications some new limits for special means of positive real numbers are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.

In many stock disintegration issues of the real world, the decay pace of certain things might be influenced by other contiguous things. Depending on the situation, the influence of weakened items can be reduced by eliminating them through examination. We specify a model that impacts the average monthly cost, and the non-linear programming Lagrangian method is solved the specified model. The fuzzify inventory model is used to determine the lowest cost by employing a trapezoidal fuzzy number, and the defuzzification process is performed using the graded mean integration representation method. To test the model, we created a CSV file, used PYTHON (version 3.8.5), we developed a program to predict the economic order quantity and total cost.

In this paper, we introduce $\lambda_{(s,\varphi,\psi,L)}$-generalized Berinde type contraction and obtain some common fixed point results for such class of contractions the setting of triangular $\alpha$-admissible mappings with respect to $\eta$ in the framework of $b$-metric spaces. Our results generalize and extend some theorems in the literature. An example is given to support our result.

Our goal in this paper is to present three classes of cyclic $(\mathit{\alpha },\mathit{\beta })$- $(\mathit{\psi },\mathit{\theta },\mathit{\varphi })$-admissible multivalued mappings, and then prove the existence of fixed point in a complete metric space. Our results generalize and extend several works. Two examples were added to support our work.

In this manuscript, using the concept of multivalued contractions, some new Banach- and Caristi-type fixed point results are established in the context of metric spaces. For the reliability of the presented results, some examples and applications to Volterra integral type inclusion are also studied. The established results unify and generalize some existing results from the literature.