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Integral inequalities are the proficient aspect of mathematical analysis. Various techniques have been deployed to acquire to fresh inequalities which are beneficial in various area problems. The aim of this paper is to derive some new analytic inequalities involving generalized weighted exponential beta functions. To attain our primary objectives, we introduce the generalized exponential function X and weighted form of exponential beta functions Furthermore, we briefly discuss their properties. we derive several inequalities in association with As the applications of these new developments,we conclude some error estimates of Ostrwoski's type inequalities, which show the significance of the obtained results. [ABSTRACT FROM AUTHOR]

Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young's inequality, Hölder's inequality, Minkowski's inequality, Hermite–Hadamard's inequality, Ostrowski's inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard's inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals. [ABSTRACT FROM AUTHOR]

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the 1q and 2q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations. [ABSTRACT FROM AUTHOR]

In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of set-valued maps. These have a close relationship with symmetry analysis. One of the important aspects of the relationship between convex and symmetric analysis is the ability to work on one field and apply its principles to another. In this paper, we introduce a novel class of interval-valued (I.V.) functions called CR - γ -convex functions based on a non-negative mapping γ and center-radius ordering relation. Due to its generic property, a set of new and known forms of convexity can be obtained. First, we derive new generalized discrete and integral forms of Jensen's inequalities using CR - γ -convex I.V. functions. We employ this definition and Riemann-Liouville fractional operators to develop new fractional versions of Hermite-Hadamard's, Hermite-Hadamard-Fejer, and Pachpatte's type integral inequalities. We examine various key properties of this class of functions by considering them as special cases. Finally, we support our findings with interesting examples and graphical representations. [ABSTRACT FROM AUTHOR]

A new auxiliary result pertaining to twice ( q 1 , q 2 )-differentiable functions is derived. Using this new auxiliary result, some new versions of Hermite–Hadamard's inequality involving the class of generalized m -convex functions are obtained. Finally, to demonstrate the significance of the main outcomes, some applications are discussed for hypergeometric functions, Mittag–Leffler functions, and bounded functions. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new fractional integral identity and using this identity as an auxiliary result, some new trapezium like inequalities essentially using the class of generalized γ-convex functions are established. In order to show the efficiency of the obtained results, we discuss and present some special cases and applications. [ABSTRACT FROM AUTHOR]