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We prove a weighted $ L^{p} $ boundedness of Marcinkiewicz integral operators along surfaces on product domains. For various classes of surfaces, we prove the boundedness of the corresponding operators on the weighted Lebsgue space $ L^{p}(\mathbb{R}^{n}\times\mathbb{R}^{m}, \, \omega _{1}(x)dx, \, \omega_{2}(y)dy) $, provided that the weights $ \omega_{1} $ and $ \omega_{2} $ are certain radial weights and that the kernels are rough in the optimal space $ L(\log L)(\mathbb{S}^{n-1}\times\mathbb{S}^{m-1}) $. In particular, we prove the boundedness of Marcinkiewicz integral operators along surfaces determined by mappings that are more general than polynomials and convex functions. Also, in this paper we prove the weighted $ L^{p} $ boundedness of the related square and maximal functions. Our weighted $ L^{p} $ inequalities extend as well as generalize previously known $ L^{p} $ boundedness results.

The latest iterations of Simpson-type inequalities (STIs) are the topic of this paper. These inequalities were generated via convex functions and tempered fractional integral operators (TFIOs). To get these sorts of inequalities, we employ the well-known Hölder inequality and the inequality of exponent mean. The subsequent STIS are a generalization of several works on this topic that use the fractional integrals of Riemann-Liouville (FIsRL). Moreover, distinctive outcomes can be achieved through unique selections of the parameters.

The main objective of this article is to build up a new integral equality related to Riemann Liouville fractional (RLF) operator. Based on this integral equality, we show numerous new inequalities for differentiable convex as well as concave functions which are similar to celebrated Hermite-Hadamard and Simpson's integral inequalities. The present outcomes of this paper are a unification and generalization of the comparable results in the literature on Hermite-Hadamard and Simpson's integral inequalities. Furthermore as applications in numerical analysis, we find some means, q-digamma function and modified Bessel function type inequalities.

In this paper, we establish an integral equality involving a multiplicative differentiable function for the multiplicative integral. Then, we use the newly established equality to prove some new Simpson's and Newton's inequalities for multiplicative differentiable functions. Finally, we give some mathematical examples to show the validation of newly established inequalities.

In this paper, we obtain some new inequalities for different type of functions that are connected with the Caputo fractional derivative. We extend and generalize some important inequalities to this interesting calculus including Hermite-Hadamard inequality.

In this paper, we prove Hermite-Hadamard inequality for convex functions in the framework of h-calculus. We also use the notions of h-derivative and h-integral to prove Ostrowski's and trapezoidal type inequalities for bounded functions. It is also shown that the newly established inequalities are the generalization of the comparable inequalities in the literature. Finally, using some examples, we demonstrate the validity of newly formed inequalities and show how they can be used to special means of real numbers.

In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson's and Newton's type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.

The purpose of this paper is to establish a general stability result for a one-dimensional linear swelling porous-elastic system with past history, irrespective of the wave speeds of the system. First, we establish an explicit and general decay result under a wider class of the relaxation (kernel) functions. The kernel in our memory term is more general and of a broader class. Further, we get a better decay rate without imposing some assumptions on the boundedness of the history data considered in many earlier results in the literature. We also perform several numerical tests to illustrate our theoretical results. Our output extends and improves some of the available results on swelling porous media in the literature.

In this paper, we firstly give improvement of Hermite-Hadamard type and Fej$ \acute{e} $r type inequalities. Next, we extend Hermite-Hadamard type and Fej$ \acute{e} $r types inequalities to a new class of functions. Further, we give bounds for newly defined class of functions and finally presents refined estimates of some already proved results. Furthermore, we obtain some new discrete inequalities for univariate harmonic convex functions on linear spaces related to a variant most recently presented by Baloch et al. of Jensen-type result that was established by S. S. Dragomir.

In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, k-Riemann-Liouville (k-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel.

In this paper, making use of the q-analogue of Carlson-Shaffer operator Lq(a,c) we introduce a new subclass of spiral-like functions and discuss some subordination results and Fekete-Szego problem for this generalized function class. Further, some known and new results which follow as special cases of our results are also mentioned.

Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (α, h−m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established for the generalized convex functions. The established theorems reproduce several known results.

In this paper, the new version of the celebrated Montgomery identity is determined via quantum integral operators. By using it, certain quantum integral inequalities of Ostrowski type are established. Moreover, the relevant connection of the obtained results of this work with the derived results in previously published works is discussed.

Convex functions play a vital role in the derivation of inequalities. In this paper these functions are used to obtain certain bounds of a unified integral operator. A Hadamard inequality for these operators is established. Further bounds of several kinds of fractional and conformable integral operators are deduced in particular.

The purpose of this paper is to prove some eigenvalue inequalities involving convex functions. These extend many remarkable inequalities, most of them related to the Bellman and Aczél inequalities.

In this paper, we define a new subclass k-Q(α) of analytic functions, which generalizes the class of k-uniformly convex functions. Various interesting relationships between k-Q(α) and the class B(δ) of functions with bounded turning are derived.