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Recently, Abbas et al. [Enriched multivalued contractions with applications to differential inclusions and dynamic programming, Symmetry 13(8) (2021), 1350] obtained an interesting generalization of the Nadler fixed point theorem by introducing the concept of enriched multivalued contraction in the framework of Banach spaces. In this article, we define a new class of metrics on the family of closed and bounded subsets of a given metric space. Furthermore, fixed point theorems were established for enriched multi-valued contractions by substituting the Hausdorff metric with metrics from a specific class that are either metrically or sequentially equivalent to the Hausdorff metric. Some examples are provided to illustrate the concepts and results presented herein. These results improve, unify, and generalize several comparable results in the literature.

In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontraction of integral type mappings in the context of orthogonal metric spaces and establish some fixed point results. We construct an example to show the existence of the new type of mappings introduce in this work. Our results substantially unify, generalize and complement the comparable results in the existing literature. As an application of our results, we derive periodic point results for the generalized single valued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces.

Interval-valued maps adjust integral inequalities using different types of ordering relations, including inclusion and center-radius, both of which behave differently. Our purpose was to develop various novel bounds and refinements for weighted Hermite-Hadamard inequalities as well as their product form by employing new types of fractional integral operators under a cr-order relation. Mostly authors have used inclusion order to adjust inequalities in interval maps, but they have some flaws, specifically they lack the property of comparability between intervals. However, we show that under crorder, it satisfies all relational properties of intervals, including reflexivity, antisymmetry, transitivity, and comparability and preserves integrals as well. Furthermore, we provide numerous interesting remarks, corollaries, and examples in order to demonstrate the accuracy of our findings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce to a pair of fuzzy graphic rational F-contraction multivalued mappings and to study the necessary condition for the existence of common fixed points of fuzzy multivalued mappings in the setup of generalized parametric metric space endowed with a directed graph. A non-trivial example is presented to support the results presented herein. Our results improve and extend some recent results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is crucial in mathematical analysis. In this note, we develop various new bounds and refinements of different well-known inequalities involving Hilbert spaces in a tensor framework as well as mixed Moore norm spaces with variable exponents. The article begins with Newton–Milne-type inequalities for differentiable convex mappings. Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. To obtain all these results, we use Riemann–Liouville fractional integrals and develop several new identities for these operator inequalities. Furthermore, we present some examples and consequences for transcendental functions. Moreover, we developed the Hermite–Hadamard inequality in a new and significant way by using mixed-norm Moore spaces with variable exponent functions that have not been developed previously with any other type of function space apart from classical Lebesgue space. Mathematical inequalities supporting tensor Hilbert spaces are rarely examined in the literature, so we believe that this work opens up a whole new avenue in mathematical inequality theory. [ABSTRACT FROM AUTHOR]

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space ( l q (·) (L p (·)) ). Moreover, it was developed using classical Lebesgue space ( L p ) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of large MR-Kannan contractions on Banach space that contains the classes of Kannan, enriched Kannan, large Kannan, MR-Kannan contractions and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. We prove the existence of a unique fixed point for such a class of operators in Banach spaces. [ABSTRACT FROM AUTHOR]